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Projectile Motion Unit Student Design Cover Page(see directions on page 19)

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Projectile Motion Unit Front Page

At the end of this unit I will: q Demonstrate projectile motion calculations using vectors. q Understand the difference between linear and projectile motion. q Know that horizontal and vertical motions are independent of each other. q Be able to explain how satellites orbit earth.

Roots, prefixes, and suffixes I will understand and recognize are: Pro-, ject, vect-, vert, para

The terms I will clearly define are: Projectile, horizontal, vertical, range, vector, scalar, resolution, resultant, component,

satellite, parabola, trajectory

The assignments I will have completed by the end of the unit are:q Textbook pre-reading inventory and unit preview (pages 97-99)q More vector notes and practice (pages 102-103)q Projectile motion notes (pages 105-109)q Online project for Ch. 3 (page 110)q Review questions (pages 113-114)q Satellite notes (pages 116-117)q Bull’s eye lab (pages 118-122)q Concept development 3-1 (page 123)q Projectile problems (pages 124-126)q Study Guide (pages 127 - 129)q Concept map (page 130)q Concept cards (page 131)

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Textbook Pre-reading Inventory

Before we begin reading in the textbook, consider the statements in Column A. In Column B, rate the statement according to the scale below:

1 2 3 4 5Stongly agree Agree Neither Disagree Strongly disagree

A:

Statement

B:

Pre-reading

C:

Post-reading

D:

Pages with relevant information

1. Vector quantities have both magnitude and direction.

2. A single vector can be replaced with two components that together add up to the original vector.

3. Gravity accelerates objects in both the horizontal and vertical direction.

4. In the absence of air resistance gravity accelerates objects downward at 9.8 m/s2.

5. A satellite is continually falling around earth.

6. The angle we use to launch a projectile doesn’t matter as long as it is launched with the same initial velocity.

7. The vertical motion of an object is independent of its horizontal motion.

8. If one ball is dropped and another is thrown horizontally from the same height, they will hit the ground at the same time.

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Your teacher will instruct you to read from your textbook and return to this page to complete Column C & D.

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Chapter 3 Textbook Unit Preview

Read pages 28-39 of your textbook. As you go, complete the tasks below.

1. Explain the difference between a vector and scalar quantity in your own words. (pages 28-29)

2. Define “resolution”. (page 31-32)

3. Use the examples of projectiles given by your textbook to write you own definition of “projectile”. (page 33)

4. Write a sentence (or 2!) from your textbook that explains whether or not horizontal and vertical motion depend on each other. (pages 33-34)

5. Look at the picture on the bottom of page 36. What is the “best” angle to launch a projectile at? Why? (pages 36-37)

6. What is a satellite? (page 39)

When you are finished reading the chapter, return to the inventory on page 97 and complete columns C & D.

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Falling Coins Activity

Prediction: Read the directions below. Which coin do you think

will hit the ground first? Write your prediction in the “If… then…” format.

Directions:Place a coin at the edge of a smooth table so that it hangs over slightly. Then place a second coin on the table top some distance from the overhanging coin. Slide the second coin across the table (such as by flicking it with your finger) so that it strikes the over-hanging coin and both coins fall to the floor below.

1. What happened?

2. Repeat the activity a few more times. Did you get the same results?

3. Does the speed of the sliding coin matter? Repeat the activity a few more times, “flicking”

the coin at different speeds. What happened?

4. What outside force(s)/interaction(s) are affecting the sliding coin?

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5. What outside forces/interaction(s) are affecting the coin that is just falling?

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More Vector Practice

Draw the following vectors and complete the necessary calculations to answer the questions.

1. A car travels 250 km east before turning and travelling 200 km north. What is the car’s displacement?

2. A student walks 15 paces west, then 9 paces south. What is their total displacement?

3. A jogger runs 3 miles east, then turns north and runs for 4 miles. What is their total displacement?

4. What is the total velocity of a plane that is flying north at 100mph but is encountering a side-wind from the east of 25 mph?

5. For the vectors below, draw and label the horizontal and vertical components.

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More Vector Notes

What is a vector? Remember, a vector is an arrow used to represent

What is a resultant?Remember, a resultant is the product of _______________ two vectors

together.

What are components?When two vectors are added together to form a resultant, the two

vectors are called __________________________________.

What is resolution?

Any vector can be ____________________________ into two component

vectors at ___________________ angles to each other. The process of

determining the components of a vector is called _____________________.

What formula is helpful for combining vectors?

Use a ruler and different colors to draw and label the horizontal and vertical components of a vector.

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Projectile Motion Notes

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Projectile Motion Notes

What is a projectile?

A projectile is an object upon which the only force acting is

____________________________.

Ex. Stone thrown in the air, cannonball shot from a cannon, spacecraft

circling Earth, and a ball rolling off the edge of a table.

What are the two

components of

projectile motion?

Projectile motion has two ___________________________________ components:

_______________________________ motion

_______________________________ motion

Because these two components are _______________________________ of

each other (they do NOT depend on each other!), we can separate

them for calculations.

Describe the

horizontal motion of

a projectile.

Projectiles have a ___________________ _________________________ ____________________

in the absence of horizontal force.

Ex. When a ball rolls on a table, it rolls at a __________________________ velocity.

There is not horizontal force acting on the ball, so there is no horizontal

acceleration. Horizontal velocity is ______________________________.

Describe the vertical

motion of a

projectile.

The vertical component of projectile motion is ____________ ____________________.

It is affected by ___________________________ (at _____________ m/s2)

Due to the force of ____________________________, a projectile will

_____________________________ as it falls.

What is a parabola?

When we combine the motion in the _______________________________________ and

______________________________ directions, projectiles move in a shape called a

________________________________.

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Projectile Motion Notes

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Projectile Motion Notes

What happens when a projectile, like a cannonball, is shot at an upward angle?

Because of _____________________ the cannonball follows a _______________________ path and finally hits the ground.

What would happen if gravity didn’t affect the cannonball?

In the absence of gravity, the cannonball would follow a ______________________ ____________________ path like the image on the previous page.

The vertical distance the cannonball travels (how far above the __________________ it is) is the same distance the cannonball would fall if it were dropped from rest and allowed to fall for the same amount of ___________________.

Does the angle an object is launched at “matter”?

The launch angle ________________ matter.

At a steeper angle, there is a greater _____________________________ component

to velocity, and the projectile travels ______________________. However, since

the horizontal component is less, the ________________________ range is less.

How are launch angles related?

The same horizontal __________________ is obtained for two different projection angles if the angles add up to ______________ degrees.

The smaller angle will remain in the air for a _____________ amount of time.

The launch angle that has the greatest ________________________ ________________ is _______________ degrees.

What happens if we don’t ignore air resistance?

When air resistance is significant, the ___________________ of a projectile is diminished and the path is not a true __________________________.

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Online project for Ch.3

Visit the websites below to complete this assignment:

http://library.thinkquest.org/2779/

http://www.physicsclassroom.com/mmedia/vectors/mzi.cfm

FIRST WEBSITE:Answer the following question from the first page:

a. What did Galileo discover about the horizontal and vertical motion of a projectile?

Second Page Questions:

b. Will two balls of different masses hit the ground at the same time?

c. Look at the next picture! Why will the two balls always hit the ground at the same time?

Page 3 Question:

d. Why do they give the formula Vx=Vxo? Does the horizontal velocity, Vx, ever change?

Before you play the Water Balloon Game:

e. Predict: How will changing the velocity will change where the water balloon lands?

After you play the Water Balloon Game:

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f. Explain: What factors helped you hit the target?

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SECOND WEBSITE:

Before you look at each animation

Predict: What will happen in each of the following scenarios?

After you look at each animation

Explain: What happened in each of the following scenarios?

Throwing food to the monkey in a gravity free environment:

Throwing food above the monkey with gravity on:

Throwing food to the monkey at fast speed:

Throwing food to the monkey at slow speed:

Throwing food to the monkey in a gravity free environment:

Throwing food above the monkey with gravity on:

Throwing food to the monkey at fast speed:

Throwing food to the monkey at slow speed:

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Review Questions

1. How does a vector quantity differ from a scalar quantity?

2. Why is speed classified as a scalar quantity and velocity classified as a vector quantity?

3. If a vector that is 1 cm long represents a velocity of 10 km/h, what velocity does a vector of

2 cm long drawn to the same scale represent?

4. Why does a bowling ball move without acceleration as it rolls along a bowling alley?

5. In the absence of air resistance why does the horizontal component of velocity for a

projectile remain constant while the vertical component changes?

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6. How does the downward component of the motion of a projectile compare with the motion

of free fall?

7. At the instant a ball is thrown horizontally over a level range, a ball held at the side of the

first is released and drops to the group. If air resistance is neglected, which ball strike the

ground first?

Review Questions

8. At what angle should a slingshot be oriented for maximum altitude? For maximum

horizontal range?

9. Neglecting air resistance, if you throw a ball straight up with a speed of 20 m/s, how fast

will it be moving when you catch it?

10. What do we call a projectile that continually “falls” around earth?

11. How fast must a projectile moving horizontally travel so that the curve it follows matches

the curve of earth?

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12. Why is it important that such a satellite be above Earth’s atmosphere?

13. What force acts on a satellite that is above Earth’s atmosphere?

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Satellite Notes

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Satellite Notes

What is a satellite?

A satellite is simply a __________________________________ moving fast

enough to fall ______________________ earth rather than into it.

When an object is in ________________, the Earth curves away from

underneath the object at the same rate as it ______________. The object

thus falls continuously but never hits the ____________________________.

What speed does a

satellite need to be

moving to orbit earth?

What is another term for

this speed?_______________________________ velocity.

What happens to most

objects at this speed?

______________________________________________ burns or melts most objects

at this speed.

Are satellites free from

gravity?

______________________. Air resistance is almost totally absent, but gravity

______________________________________________________________________________.

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Bull’s Eye Lab – Flow Chart

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Bull’s Eye Lab – Data

Horizontal speed:

Distance (A to B) Time Speed

Trial #1

Trial #2

Trial #3

Average: (vx)

Distance (y):

Height from bottom of ramp to top of target: (dy)

Time:

Equation to find vertical distance (should relate dy and t):

Rearrange to solve for t:

t =

Distance (x):

Equation to find horizontal distance (should relate dx and t):

Rearrange to solve for dx :

dx :

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Bull’s Eye Lab – Procedure

Purpose: To investigate the independence of horizontal

and vertical components of motion and to predict the landing point of a projectile.

Discussion: Imagine a universe without gravity. In this

universe, if you tossed a rock where there was no air, it would just keep going – forever. Because the rock would be going at a constant speed, it would cover the same amount of distance in each second. The equation for distance traveled when motion is uniform is:

The speed is:

Coming back to earth, what happens when you drop a rock? It falls to the ground and the distance it covers in each second increases. Gravity is constantly increasing its speed. The equation for the vertical distance dy fallen after any time t is:

where g is the acceleration of gravity. The falling speed v after time t is:

What happens when you toss the rock sideways? The curved motion that results can be described as the combination of two straight-lined motions: one vertical and the other horizontal. The vertical motion undergoes the acceleration due to gravity, while the horizontal motion does not. The secret to analyzing projectile motion is to keep two separate sets of “books”: one that treats the horizontal motion according to

And the other that treats the vertical motion according to

Horizontal motion When thinking about how far, think about dx =vt When thinking about how fast, think about v = dx/t

Vertical motion When thinking about how far, think about dy = ½ gt2

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When thinking about how fast, think about v = gt

Bull’s Eye Lab – Procedure

- Your goal in this experiment is to predict where a steel ball will land when released from a certain height on an incline. The final test of your measurements and computations will be to position an empty soup can so that the ball lands in the can the first time!

Procedure:1. Assemble your ramp. Make it as sturdy as possible so the steel ball rolls smoothly. The ramp

should not sway or bend. The ball must leave the table horizontally. Make the horizontal part of the ramp at least 20 cm long. The vertical height of the ramp should be at least 30 cm.

2. Use a stopwatch to measure the time it takes the ball to travel from point A to point B in the diagram. Record this time on your data sheet and calculate the average horizontal speed. Do not allow the ball leave the table or hit the floor!

3. Repeat step #2 two more times. On the data sheet find an average horizontal speed.

4. Measure the vertical distance that the ball must drop from the bottom of the ramp in order to land in the target. Be sure to measure to the top of the target, not all the way to the floor. Record this distance on your data sheet.

5. Choose an equation to calculate the time it takes the ball to fall from the bottom end of the ramp to the target. (hint: this equation must relate dy and t). Write this equation on your data sheet and calculate the time.

6. The range is the horizontal distance that a projectile travels. Predict the range of the ball by calculating it on your data sheet.

7. Show your calculations to your teacher. Once approved, you’ll receive a ball to test your prediction.

8. Measure and place the target in your predicted range. Roll te ball down the ramp and see if you were right!

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Bull’s Eye Lab – Conclusions

Answer the following conclusion questions with your group. Be sure to include the answers to all of these questions in your lab report!

1. What may cause the ball to miss the target?

2. Why can we ignore air resistance for a ball bearing but not for some other objects?

3. Were you able to catch the ball? If not calculate your percent error using the equation below.

(Distance your ball fell – distance you calculated)(Distance you calculated)

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X 100%Percent error =

Concept Development 3-1

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Projectile Problems

1. A ball rolls off a 1.0 meter high table and lands on the floor 3.0 meters away from the table. A. How long is it in the air?

B. With what horizontal velocity did the ball fell off the table?

C. What is the vertical velocity of the ball just before it hits the floor?

D. What is the horizontal velocity of the ball just before it hits the floor?

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Projectile Problems

2. A carpenter tosses a shingle off a 9.4 m high roof, giving it an initial horizontal velocity of 7.2 m/s.

A. What is the final vertical velocity of the ball?

B. How long does it take to reach the ground?

C. How far does it move horizontally this time?

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Projectile Problems

3. A tiger leaps horizontally from a 12 m high rock with a speed of 4.5 m/s. How far from the base of the rock will she land?

4. An arrow fired horizontally at 41 m/s travels 23 m horizontally before it hits the ground. From what height was it fired?

5. A ball is thrown horizontally from the roof of a building 50. m tall and lands 45 m from the base. What was the ball’s initial speed?

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Projectile Motion Study Guide

Part 1: Reviewq Look through all of the pages in this unit. Is there anything you did not complete? Finish it

now as extra practice for the test. q Look back over your Cornell notes for this unit. Cover the right half of the page and see if

you can answer the questions on the left. Study any information you cannot answer without peeking at the right side.

q Use your concept cards to study key terms. q Practice rearranging the equations we used this unit. Determine the most important ones

and include them on your “cheat sheet”.q Read the summaries you wrote for each set of notes. Underline important or key terms.

Part 2: Practice1. Define the following terms in your own words:

a. Vector

b. Projectile

c. Horizontal

d. Vertical

e. Range

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f. Component

g. Trajectory

Projectile Motion Study Guide

2. How are the vertical and horizontal components of projectile motion related?

3. What formulas do you use to find distance, velocity (speed), and time for vertical motion?

4. What formulas do you use to find distance, velocity (speed), and time for horizontal motion?

5. A ball is projected horizontally with an initial velocity of 20 m/s east, off a cliff 100 meters high. How many seconds does the ball take to reach the ground?

6. If thrown horizontally from the same height, which will hit the ground sooner: a ball thrown at 10 m/s or a ball that was just dropped? Why?

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7. A force of 6.0 Newtons north and a force of 8.0 Newtons east act concurrently on an object. What is the magnitude of the resultant of the two forces?

Projectile Motion Study Guide

8. Calculate the magnitude of the resultant of the vectors below:

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9.

Projectile Motion Unit Concept Map(see page 19 for directions)

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Projectile Motion Unit Concept Cards(see pages 13-14 for directions)

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Projectile Motion Unit Back Page

The California Dept. of Education Standards I have come to understand are:

q a. Students know how to solve problems that involve constant speed and average speed.

q i.* Students know how to solve two-dimensional trajectory problems.q j.* Students know how to resolve two-dimensional vectors into their components

and calculate the magnitude and direction of a vector from its components.

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