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PHYSICS 30: Gravity & Projectile Motion – Acceleration of GravityPART A: Ball Drop1. Measure a drop distance for a ball.2. Drop the ball and measure the time of the drop.

a. Use several timers for each drop. b. Do several trials for each drop height.c. Do several drop heights.

3. Calculate the object’s acceleration using a Kinematics equation.

HEIGHT AVG. TIME ACCELERATION1.1.1.2.2.2.3.3.3.

PART B: Ramp Roll1. Measure and record the length of a ramp2. Roll a ball down the ramp3. Measure the length of time it takes the ball to roll the length of the ramp4. Measure the length and height of the ramp. This information will be used to

determine the angle the ramp5. Draw a vector diagram for the acceleration of gravity and two components,

one parallel to the ramp and one perpendicular to the ramp

Ramp length

Ramp time

Ramp height Acceleration

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PHYSICS 30: Gravity & Projectile Motion – Projectile Motion

A ball is rolled off the top of a tall building with a horizontal velocity of 3 m/s The instant the ball rolls of the top of the building it begins falling because of

gravity. Gravity has an acceleration of 9.8 m/s2 [Dn]. Calculate the horizontal distance the ball travels for each second of time. Calculate the vertical distance the ball has fallen for each second of time.

TIME (s) 1 2 3 4 5 6 7 8Horizontal Distance:dH (m)Vertical Distance:dV (m)

On the top of the graph show the horizontal distance for each time. On the left side of the graph show the vertical distance for each time. Combine the horizontal and vertical distances to show the path the ball follows

as it falls.

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PHYSICS 30: Projectile Motion – Internet Activity

Us the internet to access the website: http://www.walter-fendt.de/ph14e/projectile.htm Fill in the chart and answer the Analysis Questions Set the initial height to zero. Select “slow motion” Velocity information can be obtained by clicking on the velocity button

VELOCITY ANGLE MAXIMUM DISTANCE

MAXIMUM HEIGHT

END VELOCITY

TOTAL TIME

CONSTANT LAUNCH VELOCITY50 550 1550 2550 3550 4550 5550 6550 7550 85

CONSTANT LAUNCH ANGLE10 4520 4530 4540 4550 45

Analysis Questions:1. Constant Launch Velocity:

a) At what angle does the maximum distance occur?

b) At what angle does the maximum height occur?

c) At what angle does the maximum time occur?

d) What “rule” could you suggest about the relation between angle and maximum distance?

e) What “rule” could you suggest about the relation between angle and total time?

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2. Constant Launch Angle:a) As the launch velocity increases, what happens to the maximum

distance?

b) As the launch velocity increases, what happens to the maximum

height?

c) As the launch velocity increases, what happens to the total time in the

air?

d) What effect does the launch angle have on the end velocity?

3. Velocity components: a) The object has the same launch and end velocity, does the velocity of

the object stay the same while it is in the air?

b) When the object reaches its maximum height, what vertical velocity does it have?

c) What happens to the vertical velocity while the object is in the air? (run with the velocity button selected

d) What happens to the horizontal velocity while the object is in the air? (run with the velocity button selected)

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PHYSICS 30: Gravity & Projectile Motion – ExamplesThere are five different types of questions: Dropping straight down. Going straight up and then straight down. Only initial horizontal velocity. Both initial horizontal and vertical velocity (take off and land at the same

height). Both initial horizontal and vertical velocity (take off and land at different

heights).

1. A person drops a Loonie coin from a 10th floor apartment balcony 34 metres above the ground.a) Draw a sketch of this situation and include information.b) How long will it take the Loonie to hit the ground?c) How fast will the coin be traveling when it hits the ground?d) Has the coin fallen half the distance in half the time? Explain.

2. A flare is shot straight up into the air with an initial velocity of 40 m/s.a) Draw a sketch of this situation and include information.b) How high does the flare travel?c) How much time does it take the flare to reach its maximum height?d) The flare lasts for 6 seconds before burning out. How high is the flare when

it burns out?

3. A kid runs off the 10 metre tower at the Lawson Pool. The 10 metre tower is 10 metres above the water. The kid is running at a velocity of 5 m/s when he runs off the tower. Only a kid would run off this tower!a) Draw a sketch of this situation and include information.b) How far does the kid travel horizontally before hitting the water?c) If he ran faster, what difference would that make to his “jump”?

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4. Mike Weir hits a golf ball with a velocity of 50 m/s at an angle of elevation of 40. He hits the ball in Saskatchewan so that it takes off and lands at the same height.a) Draw a sketch of this situation and include information.b) Draw a diagram showing the horizontal and vertical components of the

initial velocity.c) What is the maximum height reached by the golf ball?d) How much time is the golf ball in the air?e) What distance from Mr. Weir does the golf ball land?f) Is this the maximum distance the ball could have traveled with the same

initial speed?

5. An archer shoots a flaming arrow towards a castle. The archer is standing 130 metres from the castle. The arrow is released at an angle of 45 with a velocity of 40 m/s. The castle walls are 25 metres high.a) Draw a sketch of this situation and include information.b) Does the arrow clear the castle wall or hit the side of the wall? Calculate

and explain.

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PHYSICS 30: Projectile Motion – Sling Shot Launch NAME:

DISTANCE TIME

m sec

Show your work for the calculation of the following for your Sling Shot Launch:

1. Maximum vertical height2. Initial vertical velocity3. Initial horizontal velocity4. Launch angle5. Initial launch velocity (combination of vertical and horizontal)

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PHYSICS 30: Gravity & Projectile Motion – Homework Assignment

1) A water balloon is dropped from the top of a grain elevator, a distance of 85 metres.a) How long does it take the water balloon to reach the ground?b) What is the velocity of the water balloon when it impacts on the ground?c) What is the average velocity of the water balloon on its way to the

ground? d) Does the water balloon reach this average velocity at half the height or half

the time? Same question posed another way, what is the velocity of the water balloon at: half the time and half the height?

2) A slingshot is used to fire a rock straight up with an initial velocity of 45 m/s [up].a) What is the magnitude and direction of the acceleration of the rock:

i) on the way upii) at its maximum heightiii) on the way down?

(1)How do you know each value?b) What time is required for the rock to reach its maximum height?c) What is the rock’s maximum height?d) What are the rock’s two velocities when the height of the rock is ½ its

maximum height? Why are there two values and how are they different?

3) Bugs Bunny watches Yosemite Sam walk off the end of the high diving board 120 metres above the water tank. He then realizes that there is no water in the tank. 1.5 seconds after Sam has jumped Bugs throws down a bucket of water with an initial velocity of 25 m/s [down].a) How much time does it take Yosemite Sam to reach the tank below the high

diving board?b) How much time does it take the water to reach the tank?c) Does the water arrive before or after Sam? Explain.d) Why does Yosemite Sam miss the tank? (This is more of a philosophical

question rather than a physics question.)

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4) Wiley E. Coyote is flying at a height of 500 metres. Mr. Coyote is flying at a velocity of 45 km/h [east] when he lets go of a bomb. Wiley is attempting to drop the bomb on the Road Runner who is standing stationary on the ground.a) Explain what is wrong with the

motion of the bomb and coyote as shown in the diagram showing the coyote’s plan.

b) How far from the Road Runner should the bomb be dropped so that it lands in the immediate vicinity of the Road Runner?

5) Wiley E. Coyote runs off a cliff while chasing the Roadrunner. It takes Mr. Coyote 7.5 seconds to hit the ground below the cliff. He “touches” down at a distance of 64 metres away from the base of the cliff.a) What is the height of the cliff?b) What was Wiley E’s initial velocity off the cliff?c) What do we call the two parts the fall that the cartoonist cleverly shows?

What do we know about the time of each part?

6) An arrow is shot into the air at an angle of 60 up from the ground. The arrow has an initial velocity of 50 m/s.a) Draw a diagram showing the horizontal and vertical components of the

initial velocity of the arrow.b) Calculate the horizontal and vertical components of the initial velocity.c) What happens to the values of the horizontal and vertical velocities while

the arrow is traveling through the air?d) What length of time is the arrow in the air?e) How far away from the archer does the arrow land?

7) A water balloon is launched from a three-person slingshot so that it remains in the air for 4.24 seconds. The balloon lands 128.6 metres from where it was launched. Calculate the initial velocity and the angle at which the balloon was launched.

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8) A cannon is located at the top of a castle, 65 metres above the ground. The cannon fires a cannon ball with an initial velocity of 40 m/s at an angle of 45 up from the horizontal.a) What is the maximum height reached by the cannon ball?b) How much time does it take the cannon ball to reach its maximum height?c) How much time does it take the cannon ball to fall to the ground from its

maximum height?d) How far from the castle does the cannon ball hit the ground?

9) A golfer hits a golf ball so that it has an initial velocity of 48 m/s at an angle of 40 up from the ground. The golfer is standing 200 metres from large evergreen tree that is 14 metres tall. If the ball is hit straight in line with the tree will the ball:

i) Pass over the tree?ii) Hit the tree?iii) Land before it reaches the tree?

Explain your reasoning with calculations.

10) The world record for the long jump is 8.95 metres set by Mike Powell. Mr. Powell was capable of running at a speed of 20 m/s during the run-up for a long jump. A long jumper gets as much speed as they can in their run-up and then jumps up in the air as high as they can. a) Calculate his initial take off velocity (horizontal and vertical combined). b) Calculate the angle that he jumped at for his record setting jump.

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Gravity & Projectiles – Homework Assignment Answers

1a) t = 4.16 sb) vf = 40.82 m/sc) vavg = 20.4 m/sd) half the time

2a) 9.8 m/s2 [down] – gravity doesn’t changeb) t = 4.59 sc) d = 103.3 md) vf = ± 31.8 m/s

3a) t = 4.95 sb) vf = 54.6 m/s, t = 3.02 sc) water beats Samd) LOL

4 a) Bomb should be directly underneath Coyoteb) d = 126.25 m b/c t = 10.1 s

5a) d = 275.6 mb) v = 8.53 m/sc) horizontal and vertical components, time is the same for both

6

a) 50 m/s VV 60° VHb) vv = 43.3 m/s vH = 25 m/sc) vH is a constant, vV is decreasing due to gravityd) t = 8.84 se) d = 221 m

7 v = 36.8 m/s at 34°

8a) d = 40.8 m ( or d = 105.8 m)b) t = 2.89 sc) t = 4.65 sd) d = 213.2 m

9The golf ball passes over the tree

the height at dH=220 m is dV=22.8 m or when dV= *** m, the dH=*** m

10 v = 20.12 m/s at 6.3°

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PHYSICS 30: Projectile Motion – Review1. A 3-person slingshot is used to shoot a water balloon towards a castle

surrounded by a 5 metre wall. The water balloon is launched with an initial velocity of 30 m/s at an angle of 55º. The balloon is launched from a distance of 85 metres from the wall. Sketch the situation. What are the initial horizontal and vertical components of the water

balloon’s velocity? (vh=17.2m/s vv=24.6 m/s) What is the maximum height reached by the water balloon?(30.8 m) What is the time it takes to reach the maximum height?(2.5 s) How much time does it take to fall to a height 5 metres above the

ground?(4.79s) How much time does it take to travel horizontally 85 metres?(4.9s) Does the water balloon clear the wall or does it hit the wall? How do you

know?(Hits the wall, height at 4.9 s = 2.7 m) (Hits the wall, 4.79s<4.9s) How far would the water balloon travel if there were no wall and just a

flat field?(86 m) What difference would increasing the launch angle to 70º make to the

horizontal and vertical motion?(vh=10m/s & vv=28.2 m/s: the balloon would travel higher, spend more time in the air, but travel a lesser horizontal distance)

2. While chasing the Roadrunner, Wil E. Coyote runs off of a cliff at a speed of 30 m/s. The cliff turns out to be 110 metres high. How far from the base of the cliff does the coyote hit the ground?(141m,

t=4.7s) How fast is the coyote travelling vertically when he hits the ground?

(46.1m/s)

3. An arrow is shot into the air at an angle of 50 up from the ground. The arrow has an initial velocity of 65 m/s. How far away does the arrow land.(419m, vh=41.9m/s, vv=49.8m/s, t=10.2s)

4. A cannon is used to launch a 3 kg projectile straight up a distance of 800 metres. The cannon has a barrel with a length of 1.2 metres. The projectile accelerates the entire time it is in the barrel of the cannon. What is the initial velocity of the projectile as it leaves the end of the

barrel of the cannon?(125.3m/s) What is the acceleration of the projectile at its maximum height?

(9.8m/s2[Down]) What is the velocity of the projectile when it is at a height of 400 metres?

(±88.6m/s)

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PHYSICS 30: Review Online - http://www.physicsclassroom.com/reviews#vectors

Multiple Choice343536383942434445

Diagramming

51

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*

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Word Problems

60

vix (m/s) y (m) t (s) x (m)a 15.0 m/s 20 mb 15.0 m/s 3.00 sc 45.0 m 45.0d 2.50 s 30.0e 74.0 m 66.0

62 dH =

63a) t=b) dv at max height=c) dH =

6466 a) b)

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