4 Projectile Motion Name

Reading: GALILEO EXPLAINS PROJECTILE MOTION

In this investigation, you have studied the phenomenon of projectile motion. Perhaps you

found it rather difficult to deal with the fact that an object projected into space has two

simultaneous motions - each totally independent of the other. Indeed the idea of constant

velocity and constant acceleration being present in the same object at the same time is

paradoxical. If it makes you feel any better, you are not alone in your confusion. In fact,

people of great wisdom denied the simultaneous motions of a projectile for many centuries.

In the sixteenth century it was reasoned that an object fired from a cannon had two distinct

motions. First, the object would have motion resulting from the explosion of the

gunpowder, then it would fall to the ground due to its natural motion. In other words, the

cannonball would move in the direction it was fired until the gunpowder's effect was gone,

then it would fall straight to the earth. The path would look something like Figure 1.

But, Galileo, a great sixteenth century physicist, proposed a quite different

hypothesis. He determined that the force of the gunpowder was applied

only at the instant of the explosion; the result of that force was the

constant velocity of the ball. As soon as the ball left the cannon, the force

of gravity began to cause the ball to accelerate toward the earth at a

constant rate. He proposed that the path of the ball would look like Figure

2.

The actual path follows a curve called a parabola. If you carefully

watched how balls were thrown during the lecture about two-dimensional

motion, you will have seen this yourself.

So, now that you are convinced that objects moving through space follow curved parabolic paths

due to the simultaneous presence of constant horizontal velocity and constant vertical

acceleration, what good is this knowledge? Well, we've already mentioned one important use

(although not an altogether pleasant one) - the firing of projectiles of war. Like the ancient

catapults and cannons, modern artillery and bombs must be aimed with the ultimate path of the

object in mind. You can determine the horizontal distance covered by a fired object and predict

its vertical motion using the knowledge of vectors you gained in investigation 2.

Another interesting consequence of the simultaneous motions of bodies in flight had much historical significance. Think - if

you drop a coin from the top of a tall ladder, where would it land? Better yet, if you dived from a diving board into a

swimming pool situated on a moving ship, would you land in the pool or on the deck of the ship? How silly, you say! The

coin would drop at the base of the ladder and you would land in the pool. But, now consider that the earth is moving at all

times. So, the free-falling coin leaves your hand while the ladder is in one place and lands on the ground after the ladder has

moved a bit due to the motion of the earth. Likewise, you dive from the diving board when the pool is in one position and

land after the boat has moved due to its own power as well as the motion of the earth. Well now, are you still sure of your

initial response?

Aristotle, a scientist of ancient Greece, and Galileo differed in their ideas

concerning this issue as well as the motion of falling bodies. Aristotle used

this very issue as evidence that the earth did not move. If the earth had

motion of its own, he reasoned, then an object dropped from the mast of a

ship would fall into the sea because the ship would move out from under the

object. (He never tested this, by the way.) If Aristotle had been right, you

would not want to practice your diving on a moving ship!

On the other hand, Galileo argued that an object dropped from the top of a

ship's mast would land at the base of the mast because, while the object was falling vertically, it also participated in the

horizontal motion of the ship and earth. Thus, a falling object had vertical motion due to the effect of gravity and also

retained any horizontal motion initially given to it. This eventually led to the concept of inertia which we will later study in

greater detail.

Figure 2

Figure 3

Figure 4Figure 5

Figure 6

Figure 7

Figure 1

Reading: TRAJECTORIES

You have learned that any object that is projected by some

means and continues in motion (free-fall) is a projectile.

Falling bodies are a special case of projectile motion.

Projectile motion can also occur in two dimensions: the

projectile can move both horizontally and vertically. You

have also learned that the horizontal and vertical motions

of a projectile are independent.

Another important aspect of projectile motion is the path,

or trajectory of the object. The trajectory of a projectile is

curved; it is parabolic. This curved path is due to the

object's constant horizontal velocity and its changing

vertical velocity. Figure 3 shows vectors representing both

horizontal and vertical components (or parts) of velocity for a

projectile following a parabolic trajectory.

Notice that the horizontal component is always the same, and

only the vertical component changes. Note also that the

actual or total velocity is represented by the resultant vector

of the horizontal and vertical components. In other words, the

actual velocity can be found by vector addition of the

horizontal and vertical portions of that velocity. At the top of

the arc the vertical component vanishes to zero (vf vertically

is zero). This means that the actual velocity at that point is

the horizontal velocity alone. Everywhere else the magnitude

of velocity is greater.

Figure 4 shows the trajectory of a projectile with the same

launching speed at a steeper angle. Notice that the initial

velocity vector has a greater vertical component than when

the projection angle is less. This greater component results in

a higher path. But the horizontal component is less so the

range (horizontal distance) is less.

Figure 5 shows the trajectories of several projectiles all having

the same initial speed but different projection angles. The

figure neglects the effects of air resistance, so the paths are all

parabolas. Notice that these projectiles reach different altitudes

and have different ranges. It is interesting to note that two

different angles can result in the same range (compare 60 to

30 or 75 to 15 ).

Note how maximum range is attained at an angle of 45 . This

holds true for such sports as baseball - the ball travels farthest if

it is batted at 45 . (This does not work when the projectile is

similar in weight to the force applied to it. Then the best range

is achieved at angles much less than 45 .)

–

to 1 .

Figure 3

Figure 4

Figure 5

44 PPrroojjeeccttiillee MMoottiioonn Name

Worksheet A: Applying the Readings Write the letter corresponding to the best answer in the blank at the left of each question.

1. Which of the following would NOT be considered a projectile?

a. A cannonball fired towards a distant castle.

b. A cannonball rolling down a slope.

c. A cannonball fired straight outward from a castle wall.

d. A cannonball after it rolls off the edge of a cliff.

2. The horizontal component of a projectile's velocity is independent of...

a. the vertical component of its velocity.

b. the range of the projectile.

c. time.

3. In the absence of air friction, which component of a projectile's velocity will not change as the projectile

moves?

a. vertical b. horizontal c. both vertical and horizontal

4. At the instant a ball is thrown horizontally with a large force, an identical ball is dropped from the same

height. Which ball hits the ground first?

a. the projected ball b. the dropped ball c. neither - they hit simultaneously

5. A ball is thrown up and forward into the air. At the very top of the ball's trajectory, its actual velocity is...

a. entirely horizontal.

b. entirely vertical.

c. both vertical and horizontal.

d. zero.

6. In the absence of air resistance, the angle at which a projectile will go the farthest is...

a. 75 b. 60 c. 45 d. 30

7. A ball thrown in the air will never go as far as physics ideally would predict because...

a. one can never throw the ball fast enough.

b. gravity is acting.

c. ideally the ball would never land.

d. air friction slows the ball.

8. At what part of a trajectory does an upwardly hurled projectile have minimum speed?

a. When it is first projected.

b. Half-way to the top.

c. At the top of its trajectory.

d. When it returns to the ground.

9. A cannonball is launched from the ground at an angle of 30 degrees and a speed of 20 m/s. Ideally (no air

resistance) the ball will land on the ground with a speed of...

a. 40 m/s b. 20 m/s c. 10 m/s d. 0 m/s

10. A bullet fired horizontally hits the ground in 0.5 second. If it had been fired with a much higher speed in

the same direction, it would have hit the ground (neglecting the Earth's curvature and air resistance) in...

a. 0.5 s b. less than 0.5 s c. more than 0.5 s

11. A projectile is fired horizontally above the surface of the moon (which has no atmosphere). The

projectile maintains its horizontal component of speed. This is because the object...

a. is not acted upon by any forces after it is fired.

b. is not acted on by horizontal forces after it is fired.

c. has no vertical speed to begin with.

d. is not acted upon by gravity.

12. An object is dropped and falls freely to the ground with an acceleration of 1 g (1 g = 9.8 m/s2). If it is

thrown upward at an angle instead, its free-fall acceleration would be...

a. 0 g b. 1 g downward c. 1 g upward d. larger than 1 g

13. A ball is hurled into the air at an angle of 30 degrees and lands on a target that is at the same level as

that where the ball started. The ball will also land on the target if it is thrown at an angle of...

a. 40 degrees b. 45 degrees c. 55 degrees d. 60 degrees

14. A rifle with a muzzle velocity of 100 m/s is fired horizontally from a tower. Neglecting air resistance,

where will the bullet be 1.00 second later?

a. 50.0 m downrange b. 98.0 m downrange c. 100. m downrange d. 490 m downrange

15. After a rock that is thrown straight up reaches the top of its path and is starting to fall back down, its

acceleration is (neglecting air resistance)...

a. greater than when it was at the top of its trajectory.

b. less than when it was at the top of its trajectory.

c. the same as when it was at the top of its trajectory.

16. Suppose that you are an accident

investigator and you are asked to

determine whether or not the car was

speeding before it crashed through the

rail of the bridge and into the mud

bank, as shown. The speed limit at the

bridge is 50.0 mph which is 22.4 m/s.

What is your conclusion? Show your

work.

4 Projectile Motion Name

44 PPrroojjeeccttiillee MMoottiioonn Name

Worksheet B: When Projectiles Strike Trig-Based Assume air resistance is negligible and that g = ‒ 9.80 m/s

2 (or ‒ 32.2 ft/s

2). Show your work on this paper.

Work metric problems in meters and seconds and U.S. Customary System problems in feet and seconds. 1. with the horizontal, has an initial speed of 128 ft/s.

a) In how many seconds will it reach the ground?

b) How far from the point of projection will it strike? 441 feet

c) Find the angle it strikes the ground at using

2.

above the horizontal. How far above or below its original level will the ball

strike the opposite wall? 130 feet below

3. A projectile is fired upward from the top edge of a vertical 200

above the horizontal. Calculate the distance from the base of the cliff to the impact point on

the valley floor. 408 meters

4. with the vertical, releases a projectile at an altitude

of 875 m. How far does the projectile travel horizontally before striking the ground below?

5. A marble with a speed of 15.0 cm/s rolls off the edge of a table 65.0 cm high. How far, horizontally, from the

table edge does the marble strike the floor?

44 PPrroojjeeccttiillee MMoottiioonn Name

Worksheet C: Projectiles Strike Again Trig-Based Assume air resistance is negligible and that g = ‒ 9.80 m/s

2 (or ‒ 32.2 ft/s

2). Show your work on this paper.

1. with the horizontal has an initial speed of

30.0 m/s. How far from the starting point will it strike?

2. with the horizontal with an initial speed of 40.0 m/s from

the top of a cliff 150 m high.

a) In what time will it strike the ground?

b) How far from the foot of the cliff will it strike the ground?

c) At what angle with the horizontal will it strike?

USE TRIGONOMETRY INVOLVING THE FINAL VELOCITY VECTOR

3. A rifle is aimed horizontally at a target 30.0 m away. The bullet hits the target 7.50 cm below the aiming point.

What is the muzzle velocity of the rifle?

4. above the horizontal

toward a vertical cliff 365 m away. How far above the bottom does the shell strike the side wall of the cliff?

5.

above the horizontal. On the downward part of its

trajectory, it strikes a castle wall 75.0 m above the level of

the catapult. What is the horizontal distance between the

catapult and the castle?

6. A batter hits a home run at Wrigley Field. Th

above the horizontal. A fielder who has a reach of 2.00 m above the ground is backed up against the

bleacher wall, which at Wrigley Field is 118 m from home plate. The ball was 1.00 m above the ground when it

was hit. How high above the fielder's glove does the ball pass?

INQUIRY PHYSICS TEST REVIEW Name Units 1-4: One and Two-dimensional Motion (Non-Trig)

Multiple Choice Covers all topics: 1-d motion, vectors, falling bodies, projectiles. Be prepared to make or interpret distance or speed graphs of objects for ANY of the motions we have studied, including falling objects and projectiles. Know your rules of vector addition. TO PREPARE: Carefully review all of your notes and review the readings on projectiles. Study the multiple choice questions on the measurement and motion and vectors quizzes, the projectiles reading worksheet, and do the accompanying review concept questions. Problems Be prepared for a projectile problem, a falling body problem, a vector problem, and two 1-d problems with one having multiple steps (where you cannot solve for the answer directly, but must first find another given). TO PREPARE: Do the accompanying review problems. Inquiry Investigations 1-4 Test Review Assignment

Show your work on all problems, including givens, equations, and all appropriate units. Answers should be expressed with the proper number of significant figures. Assume g = - 9.80 m/s

2 and that

air resistance is negligible.

1. A stone is thrown straight downward with an initial speed of 8.00 m/s from a height of 25.0 meters.

a) Find the time it takes to reach the ground.

b) Find its impact velocity.

2. A supersonic airplane was flying horizontally with a speed of 620 m/s when a radar pod fell off. If the pod

travelled a horizontal distance of 40,300 m before it struck the ground, what was the altitude of the airplane?

20,700 m

Inquiry Physics Unit 1-4 Test Review Page 2 of 4

3. How long does it take a car to travel 50.0 m while slowing from 20.0 m/s to a stop?

4. A stone is shot upward with a speed of 20.0 m/s from a tower that is 45.0 m high, and strikes the ground at the

tower’s base. Find the impact speed of the stone.

5. The Denver Casa Bonita restaurant features cliff divers. A diver launched horizontally from the 9.00 m tall cliff

at approximately 1.20 m/s. How far away from the base of the cliff was the diver when she hit the water?

6. Phluffy the cat decides to swim across a river. The cat paddles due east at 5.0 m/s, and the river has a current of

2.0 m/s due south. Find the magnitude and direction of Phluffy's resultant velocity (in m/s) by drawing a scale

diagram. S of E

Scale:

1 cm = m/s

Resultant magnitude:

(in m/s)

Resultant direction:

(specify degrees and compass

headings)

Inquiry Physics Unit 1-4 Test Review Page 3 of 4 Write the letter corresponding to the best answer in the blank at the left of each question. Assume air resistance is negligible.

7. Which of the following quantities is a vector which changes signs (directions) when an object that was

thrown upward stops rising and begins to fall?

A. velocity B. speed C. acceleration D. time 8. A ton of feathers and a ton of bricks are dropped from the same height on the moon. What happens?

A. The feathers strike the ground first.

B. The bricks strike the ground first.

C. The feathers and bricks strike the ground simultaneously.

D. Nothing hits the ground, because there is no gravity on the moon. 9. When an object that was thrown upward reaches its highest point, which statement is true?

A. The acceleration switches from positive to negative.

B. The acceleration is zero.

C. The total displacement is zero.

D. The velocity is zero. 10. A stone is thrown upward from atop a cliff and then lands at the base of the cliff. Which statement is

true if the upward direction is considered "positive"?

A. The initial velocity of the stone is negative.

B. The acceleration of the stone is positive.

C. The final velocity of the stone is positive.

D. The final displacement of the stone is negative.

11. Victor Velocity is standing on top of the roof of his

house, firing stones with his slingshot over a level field.

He is aiming straight outward, horizontally. If Victor

pulls back harder on the sling to shoot a stone, which of

the following quantities will be changed?

A. The vertical displacement of the stone.

B. The distance the stone travels.

C. The time it takes the stone to strike the ground.

D. The stone's initial vertical velocity.

12. While riding at a constant speed on the train at the Kiddie

Park, Victor Vector playfully tossed Phluffy straight

upward. During the time Phluffy was in the air, the train

moved forward one meter. Phluffy landed...

A. in Victor’s loving arms.

B. one meter in front of Victor.

C. one meter behind Victor.

D. several meters behind Victor.

13. An object is observed and a graph of its distance versus time is constructed. The graph has a slope of

+5.00 when the distance is measured in meters and the time is measured in seconds. The object was...

A. moving at a constant speed of 5.00 m/s.

B. motionless.

C. decelerating.

D. accelerating at 5.00 m/s2.

14. Neglecting air resistance, when an object is thrown straight up, which of the following quantities is

NOT the same on the way down as on the way up?

A. acceleration B. average speed C. velocity D. time of travel

Inquiry Physics Unit 1-4 Test Review Page 4 of 4

15. Three forces simultaneously act on an object. The first is a 5 Newton force acting due east, the second

is a 3 Newton force acting due west, and the third is a 4 Newton force acting due east. What is the

resultant force?

A. 12 Newtons east B. 6 Newtons east C. 4 Newtons east D. 2 Newtons west

A stone is tossed straight upward at +9.80 m/s.

16. What is its velocity after 1.00 s?

A. +4.90 m/s B. 0 m/s C. -4.9 m/s D. -9.80 m/s

17. What is its displacement after 1.00 s?

A. +4.90 m B. 0 m C. -4.90 m D. -9.80 m

18. What is its acceleration at the top of its rise?

A. +4.90 m/s2 B. 0 m/s

2 C. -4.90 m/s

2 D. -9.80 m/s

2

Questions 19 - 22 refer to the following situation: A girl stood at first base on a level playing field and tossed a softball at

above the horizontal. It was caught by another player

over home base at the same height above the ground as it was

originally thrown.

19. At which point along its trajectory was the softball

travelling the fastest?

A. Just after it was released.

B. When it reached its maximum height.

C. Just before it was caught.

D. Both A and C are correct if there is no air resistance.

20. above the horizontal, . . .

A. it would have travelled a smaller horizontal distance.

B. it would have travelled a larger horizontal distance.

C. it would have travelled the same horizontal distance.

21. What angle of release would make the softball travel as far as possible?

A. B. C. D.

22. What was the softball's horizontal acceleration during its flight?

A. 0 m/s2 B. 2.45 m/s

2 C. 4.90 m/s

2 D. 9.80 m/s

2

23. Draw the graphs for the free-fall motion of the projectile shown at right. w its original level will the ball strike the opposite wall?

INQUIRY PHYSICS TEST REVIEW II Name Units 1-4: One and Two-dimensional Motion (Non-Trig)

In the space to the left, write the letter of the best answer to each question. Assume air resistance is negligible throughout. Answers to questions 1-8 are at the bottom.

1. An object is observed and a graph of its distance versus time is constructed. The graph has a slope of

+5.00 when the distance is measured in meters and the time is measured in seconds. The object was...

a. moving at a constant speed of 5.00 m/s.

b. motionless.

c. decelerating.

d. accelerating at 5.00 m/s2.

2. Four force vectors act simultaneously on a body as shown below. What is the resultant force?

3. The velocity (in m/s) vs. time (in s) graph of an object’s motion has a slope of +2. What does this

indicate?

A. The object will travel 2 meters each second.

B. The object is accelerating at 2 m/s2.

C. The object’s velocity is dropping by 2 m/s each second.

D. The object is rising at 2 m/s.

Questions 4 through 8 refer to the lettered sections of the graph at right. An object’s displacement as it moved backward and forward from its starting position of zero is shown. (A section can be the answer to more than one question.)

4. During which section did the object have

the largest constant speed?

5. During which section was the object always accelerating?

6. During which section was the object always moving toward its starting

position?

7. During which section was the object moving forward at a constant speed?

8. During which section was the object at rest?

Inquiry Physics Unit 1-4 Test Review II Page 2 of 2

9. A skier leaves the line at 3.00 m/sec downhill and accelerates uniformly at 1.25 m/s2 in the same direction. How

fast will the skier be moving after having gone 500 m? 35.5 m/s

10. Firemen are practicing rescue operations in which people would have to jump from tall buildings into a net. For

this training exercise, a person hurls downward from a fire escape at 5.00 m/s and falls to a net 28.4 m below the

fire escape.

a. What will be the velocity of the person at the instant he or she hits the net?

24.1 m/s down

b. How long will it take for the person to fall to the level of the net? 1.95 s

c. How long after jumping would the person reach a velocity of 9.8 m/s downward? 0.490 s

11. A bullet traveling 800.0 m/s horizontally hits a tree some distance away. If the bullet fell 0.100 m before it struck

the tree, how far away was that tree? 114 m

12. A diver ran horizontally off the edge of a sheer cliff at 4.4 m/s. If the diver hit the water exactly 8.00 m from the

base of the cliff, how high was that cliff? 16.2 m

PhysicsTest Review for Units 1 - 4 Name INQUIRY PHYSICS TEST REVIEW Name One-Dimensional Motion, Vectors, Falling Bodies, Projectiles Trig Version

Test Objectives and Study Hints

Multiple Choice Covers all topics, but stresses projectile motion concepts. Be prepared to make or interpret graphs of objects in ANY of the motions we have studied, including falling objects and projectile motion. Be prepared for questions testing your understanding of the independence of horizontal and vertical motion; review concepts behind class demos such as the simultaneous velocities apparatus, ballistic car, monkey and hunter. TO PREPARE: Read all of your notes carefully. Review the readings and worksheets on motion graphs and projectile motion. Study the multiple choice questions on the “measurement and motion” and “vectors/falling bodies” quizzes. Be sure you know the concept each questions deals with. Do the accompanying concepts check and concept review questions. Problems Be prepared for problems involving projectile motion, falling bodies, and a combination of both. For example, some falling body problems can become simple projectile motion problems testing your understanding of the independence of horizontal and vertical motion. EXAMPLE: Review Problem #9 Be prepared for a multiple-step vector problem. For example, you could be given two acceleration vectors along with a time and asked to calculate the final velocity of an object that started from rest. You would add the accelerations with vector math and then use vf=vi+at. EXAMPLE: Review Problem #10 Be prepared for a multiple-step ground-based problem. For example, sometimes the answer to one "part" of a problem becomes a given in the second "part" — you may be given information that will not directly lead to the answer, but can be used to generate another given that leads to the answer. Or, you may need to split a problem into two parts because the acceleration varies. EXAMPLE: Review Problem #12 TO PREPARE: Rework the problems on the “measurement and motion” and “vectors/falling bodies” quizzes. Rework several different types of projectile motion problem - there are about five variants. Up over level ground; dropped from height; shot angled downward from height; shot upward and land on cliff or land in valley. Do the accompanying review problems.

Physics Unit 1-4 Test Review (Trig-Based) Page 2 of 6

Practice Problems

(answers are in italics at the right margin; some of these questions were written with 2 significant figures)

1. East of South in her airplane and a speed of 100

N of E. What was the resultant velocity of her plane?

S of E

2. An angry Physics student wishes to drop an egg onto the head of poor Fred Freefall. He stations himself in a

building window 19.6 m above the level of Fred’s head. Determine how many seconds before Fred is directly

beneath him that he will have to drop the egg in order to get the desired splat.

2.00 s

3. If a stone thrown from a bridge strikes the water 10.0 m below after 1.70 s, what was the stone's initial velocity?

2.45 m/s upward

4. above the horizontal and travels 7,500 m over level

ground before hitting an enemy bunker. What was the maximum height of the shell?

1900 m

5. A skier leaves the line at 5.00 m/sec downhill and accelerates uniformly at 1.50 m/s2 in the same direction. How

fast will the skier be moving after having gone 500 m? 39.1 m/s

6. Spaced-out Sue is speeding at a constant 3.500 × 104 km/h in her space coupe when she passes a galactic cop at rest

by the side of the Milky Way. The instant Sue passes him, the cop accelerates after her at a constant rate. If it takes

him 3.000 × 105 km to catch up with her, how much was he accelerating?

8,167 km/h2

7. A ball is thrown from the top of one building toward a tall building 50.0 meters away. The initial velocity of

above the horizontal. How far above or below its original level will the ball strike the opposite

wall? 50.8 m below

8. An object travelling at 5.0 m/s speeds up by 3.0 m/s each second over a time period of 8.0 seconds. What was the

object's average speed? 17 m/s

9. A bullet is fired horizontally from a height of 78.4 m and hits the ground 1500 m away.

a) With what velocity does the bullet leave the gun? 375 m/s in the direction it was fired

b) At what angle did it strike the ground? below the horizontal

10. Phluffy can swim with a speed of 0.10 m/s in still water. One day Phluffy attempted to swim west across a part of a

river that was flowing from north to south with a speed of 0.35 m/s. What was Phluffy's displacement after

swimming for 25 seconds? S of W

11. A hose lying on the ground shoots a stream of water upward at an angle of 4 to the horizontal. The speed of the

water is 20 m/s as it leaves the hose. How high up will it strike a wall which is 8.0 m away? 5.4 m

12. NASA uses a tall research tower in Cleveland, Ohio to study falling bodies and low-gravity conditions. Items are

placed in a “drag shield” so that they will not encounter air resistance - the shield is slowed by the air, but the items

inside are allowed to move downward freely within it. An airbag at the bottom of the tower can rapidly decelerate a

package at 245 m/s2 over a distance of 0.964 m until it stops. Given this information, how far does a package drop

before striking the bag? 24.1 m

Physics Unit 1-4 Test Review (Trig-Based) Page 3 of 6

Concept Check (see reverse for answer analysis)

13. Two metal balls are the same size, but one weighs twice as much as the other. The balls are dropped from the top of a two story building at the same instant of time. The time it takes the balls to reach the ground below will be...

A. about half as long for the heavier ball. B. about half as long for the lighter ball. C. about the same time for both balls. D. considerably less for the heavier ball, but not necessarily half as long. E. considerably less for the lighter ball, but not necessarily half as long.

14 . A bowling ball accidentally falls out of the cargo bay of an airliner as it flies along in a horizontal direction (to the right as shown in the diagram). As seen from the ground, which path would the bowling ball most closely follow after leaving the airplane?

15. Two steel balls, one of which weighs twice as much as the other, roll off a horizontal table with the

same speeds. In this situation... A. both balls hit the floor at approximately the same horizontal distance from the base of the table. B. the lighter ball travels twice the horizontal distance from the table base than does the heavier ball. C. the heavier ball travels twice the horizontal distance from the table base than does the lighter ball. D. the lighter ball travels quite a bit farther from the table base than the heavier, but not necessarily

twice as far. E. the heavier ball travels quite a bit farther from the table base than the lighter, but not necessarily

twice as far.

16. The position of two blocks at successive 0.20 second time intervals are represented by the numbered squares in the diagram at right. The blocks are moving toward the right.

Do the blocks ever have the same speed? A. No. B. Yes, at instant 2. C. Yes, at instant 5. D. Yes, at instant 2 and 5. E. Yes, at some time during interval 3 to 4.

17. The position of two blocks at successive tim e intervals are represented by the numbered squares in the diagram at right. The blocks are moving toward the right.

The acceleration of block A is... A. larger than that of block B. B. greater than zero and equal to that of block B. C. less than that of block B. D. zero, as is that of block B.

18. The motion of an object after it is released until it is caught is graphed as shown at right. Which situation corresponds to the graphs? (Assume air resistance is negligible.)

A. An object thrown straight upward which is caught below its starting point.

B. An object thrown straight downward which bounces and is caught below its starting point. C. An object thrown upward at some angle to the horizon which is caught below its starting point. D. An object thrown upward at some angle to the horizon which is caught above its starting point. E. An object thrown downward at some angle to the horizon which bounces and is caught below its

starting point.

Physics Unit 1-4 Test Review (Trig-Based) Page 4 of 6 Concept Check Analysis: 13. The correct answer is C. All objects fall with the same acceleration rate (same rate of velocity change) in the

absence of air resistance. Even with air resistance, objects of the same size and shape can be presumed to encounter about the same drag.

Possible Misconceptions for Wrong Answers A: Mistaken belief that heavier objects fall faster than lighter ones. B or E: Possible mis-reading of question or answers. D: Mistaken belief that heavier objects fall faster than lighter ones, or misinterpretation of the effect of air

resistance. 14. The correct answer is D. A projectile will follow a parabolic path, and is immediately acted upon by gravity upon

release. Possible Misconceptions for Wrong Answers

A or B: Mistaken belief that mass makes things stop, or failure to realize that a projectile has same initial velocity as the projector.

C: Failure to realize that the vertical velocity of a projectile in free-fall will change. E or F: Failure to realize that a projectile is affected by gravity immediately upon release, or mistaken belief that

a projected object receives some sort of “impetus” that slowly disappears.

15. The correct answer is A. The horizontal velocity of a projectile is constant (its changing vertical motion will not directly affect its horizontal motion) and all objects fall with the same acceleration rate in the absence of air resistance. Even with air resistance, objects of the same size and shape can be presumed to encounter about the same drag.

Possible Misconceptions for Wrong Answers B: Mistaken belief that heavier objects fall faster than lighter ones, or that lighter projectiles are not affected as

quickly by gravity. C Mistaken belief that heavier projectiles retain their horizontal motion better than lighter ones. Possible mis-

reading of question and answers. D: Mistaken belief that heavier objects fall faster than lighter ones, or that lighter projectiles are not affected as

quickly by gravity. Also possible that the effect of air resistance was misinterpreted. E: Mistaken belief that heavier projectiles retain their horizontal motion better than lighter ones. Possible mis-

reading of question and answers, or that the effect of air resistance was misinterpreted. 16. The correct answer is E. The bottom block retains a constant speed of 4 ticks per 0.2 s time interval. The top

block is accelerating, as shown by an increase in speed (an increase in the “ticks” or distance traveled during each time interval). The top block traveled 4 ticks during the 3 to 4 time interval, so its average speed during that interval was the same as the the steady speed of the bottom block. Thus, it was moving at that speed sometime during the 3 to 4 interval.

Possible Misconceptions for Wrong Answers A: Failure to properly distinguish between velocity and acceleration, or failure to note that distance/time

indicates average speed. B or C or D: Failure to properly distinguish between displacement and velocity. The block’s position alone does

not indicate its speed. Its speed is found by examining the change in position over a time interval. 17. The correct answer is D. Both blocks are showing a steady change in distance over time, or a steady speed.

(Block A has a speed of 4 ticks per time interval; block B has a speed of 6 ticks per time interval.) An object with a constant velocity is not accelerating.

Possible Misconceptions for Wrong Answers A: Failure to note that distance/time indicates average speed. B or C: Failure to properly distinguish between velocity and acceleration, or failure to note that distance/time

indicates average speed. 18. The correct answer is D. The object is a projectile in free-fall because it has a steady horizontal velocity and a

changing vertical velocity. Its initial vertical velocity is positive, so it was projected upward. Its final vertical velocity is negative, so it ended its motion while moving downward. Its final downward speed is smaller than its initial upward speed, so it was caught before it had reached its original level (at which point it would have regained its original speed).

Physics Unit 1-4 Test Review (Trig-Based) Page 5 of 6

Additional Concept Review Questions (answers on reverse) Write the letter corresponding to the best answer in the blank. Assume no air resistance.

19. When an object that was thrown upward reaches its highest point, which statement is true?

A. The acceleration switches from positive to negative.

B. The acceleration is zero.

C. The total displacement is zero.

D. The velocity is zero.

20. While riding at a constant speed on the train at the Kiddie

Park, Victor Velocity playfully tossed Phluffy straight

upward. During the time Phluffy was in the air, the train

moved forward one meter. Phluffy landed...

A. in Victor’s loving arms.

B. one meter in front of Victor.

C. one meter behind Victor.

D. several meters behind Victor.

21. An object is observed and a graph of its distance versus time is constructed. The graph has a slope of

+5.00 when the distance is measured in meters and the time is measured in seconds. The object was...

A. moving at a constant speed of 5.00 m/s.

B. motionless.

C. decelerating.

D. accelerating at 5.00 m/s2.

22. Three forces simultaneously act on an object. The first is a 5 newton force acting due east, the second

is a 3 newton force acting due west, and the third is a 4 newton force acting due east. What is the

resultant force?

A. 12 newtons east B. 6 newtons east C. 4 newtons east D. 2 newtons west

Questions 23 - 26 refer to the following situation:

above the horizontal. It was caught by another player over home base at the same height above the ground as it was originally thrown.

23. At which point along its trajectory was the softball travelling the

slowest?

A. Just after it was released.

B. When it reached its maximum height.

C. Just before it was caught.

D. Both A and C are correct if there is no air resistance.

24. above the horizontal, . . .

A. it would have risen to a lower height than before.

B. it would have risen to the same height as before.

C. it would have risen to a greater height than before.

25. What angle of release would make the softball travel as far as possible?

A. B. C. D.

26. What was the softball's horizontal acceleration during its flight?

A. 0 m/s2 B. 2.45 m/s

2 C. 4.90 m/s

2 D. 9.80 m/s

2

Physics Unit 1-4 Test Review (Trig-Based) Page 6 of 6

Questions 27 through 31 refer to the lettered sections of the velocity vs. time graph, which is for an object moving in straight-line horizontal motion. (A section can be the answer to more than one question, but each question has only one answer.)

27. During which section was the object

accelerating forward?

28. During which section did the object

actually move backward?

29. During which section was the object

at rest?

30. During which section was the object’s acceleration always changing?

31. During which section was the object moving at a constant speed?

Questions 32 through 35 refer to the lettered sections of the displacement vs. time graph, which is also for an object moving in straight-line horizontal motion. (A section can be the answer to more than one question. Except as noted, each question has only one answer.)

32. During which section(s) was the

object at rest?

33. During which section was the

object always changing speed?

34. During which section did the object

move behind its starting point?

35. During which section was the object moving backward at a constant speed?