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PHYSICS 30: Gravity & Projectile Motion – Acceleration of Gravity
PART A: Ball Drop
1. 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
ACCELERATION
1.
1.
1.
2.
2.
2.
3.
3.
3.
PART B: Ramp Roll
1. Measure and record the length of a ramp
2. Roll a ball down the ramp
3. Measure the length of time it takes the ball to roll the length of the ramp
4. Measure the length and height of the ramp. This information will be used to
determine the angle the ramp
5. 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
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Ramp time
Ramp height
Acceleration
PHYSICS 30: Gravity & Projectile Motion – Projectile Motion
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


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)
Horizontal
Distance:
dH (m)
Vertical
Distance:
dV (m)



1
2
3
4
5
6
7
8
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
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

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
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
CONSTANT LAUNCH VELOCITY
50
5
50
15
50
25
50
35
50
45
50
55
50
65
50
75
50
85
CONSTANT LAUNCH ANGLE
10
45
20
45
30
45
40
45
50
45
MAXIMUM
HEIGHT
END
VELOCITY
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?
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TOTAL
TIME
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?
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 – Examples
There 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
DISTANCE
NAME:
TIME
m
sec
Show your work for the calculation of the following for your Sling Shot Launch:
1.
2.
3.
4.
5.
Maximum vertical height
Initial vertical velocity
Initial horizontal velocity
Launch angle
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 up
ii) at its maximum height
iii) 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
a) t = 4.16 s
b) vf = 40.82 m/s
1
c) vavg = 20.4 m/s
d) half the time
a) 9.8 m/s2 [down] – gravity doesn’t change
b) t = 4.59 s
2
c) d = 103.3 m
d) vf = ± 31.8 m/s
a) t = 4.95 s
b) vf = 54.6 m/s, t = 3.02 s
3
c) water beats Sam
d) LOL
a) Bomb should be directly underneath Coyote
4
b) d = 126.25 m b/c t = 10.1 s
a) d = 275.6 m
5
b) v = 8.53 m/s
c) horizontal and vertical components, time is the same for both
a)
50 m/s
VV
60°
6
VH
b) vv = 43.3 m/s vH = 25 m/s
c) vH is a constant, vV is decreasing due to gravity
d) t = 8.84 s
e) d = 221 m
7
v = 36.8 m/s
at 34°
a) d = 40.8 m ( or d = 105.8 m)
b) t = 2.89 s
8
c) t = 4.65 s
d) d = 213.2 m
The golf ball passes over the tree
9
 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 – Review
1. 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 Choice
34
35
36
38
39
42
43
44
45
Diagramming
*
*
*
51
*
*
Word Problems
vix
a
b
c
d
e
60
62
63
64
66
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(m/s)
y (m)
15.0 m/s
15.0 m/s
20 m
x (m)
3.00 s
45.0 m
2.50 s
74.0 m
dH =
a) t=
b) dv at max height=
c) dH =
a)
t (s)
b)
45.0
30.0
66.0