Catapult Worksheet
Projectile Motion
1. Consider throwing a ball into the air (with some angle, not straight up), what would the path of the
ball be? Sketch your idea on the following graph, label where the ball hits its maximum height and
maximum distance from the starting location:
For the following questions we will need to use a few formulas about projectile motion. An object is
considered a projectile behaving under projectile motion rules when it starts with an initial speed and
initial angle and has only the force of gravity and air resistance working upon it to bring it back to the
ground.
Definition of variables:
v0  initial speed of object at time of launch
g  9.8 m s2  32 ft s2 = gravity
  catapult launch angle
t  time elapsed from launch
h  height of ball at time t
d = horizontal distance of ball at time t
T  total time of flight (from launch to landing)
H  maximum height achieved by ball
D  total horizontal distance achieved by ball (at landing)
Projectile Motion Formulas:
To find launch angle
H tan 

D
4
:
 4H 
   tan 1 

 D 
To find initial speed
v0 
v0 of object:
gD
sin 2
2. Place and securely hold the catapult on a level surface and launch the ball, note where it lands.
Take the height measuring stick and place it at the halfway point between the launch and landing.
(You will need to measure the maximum height achieved for the next several launches.)
3. Holding the catapult steady (do not make any changes to the settings), launch the ball several
times and record the maximum height, maximum distance and time of flight. Once you have
collected data from 3 launches, average the data at the bottom of each column.
Launch
Maximum Height
Maximum Distance
Time of Flight
1
2
3
4
5
6
Average
H
D
T
4. Use the formula given above and your scientific calculator to determine the launch angle  . Show
all your work mathematically in the space provided and then put your answer in the box provided.

5. Use the launch angle
 , the formula above and your scientific calculator to find the initial speed of
your ball as it leaves the catapult,
v0 . Show all your work mathematically in the space provided
and then put your answer in the box provided.
v0 
Knowing the launch angle and the initial speed of a projectile object, we can make a graph of the path
of the projectile through the air using the following formulas to determine the x and y coordinates at
different times along the path:
x  horizontal coordinate of the ordered pair on the graph
y  vertical coordinate of the ordered pair on the graph
x   v0 cos  t and y  
g 2
t   v0 sin   t
2
6. Divide your total time from the last column of collected data above by 10. This will be your
increment of time. Fill in the table below in increments starting at 0 and increasing by the
increment determined.
Elapsed
Time
t
0
x – Coordinate
y-coordinate
x
0
y
0
7. Plot your ordered pairs
 x, y 
(x, y)
 0, 0 
on the graph below; adjust the scale on your axes as necessary.
8. Connect the points you
graphed. Was your earlier
graphical prediction about
projectile motion correct?
What type of a curve is this?
9. In order to find the launch angle of the catapult arm that will maximize the distance covered by the
ball, you will need to manipulate the formula
v0 
gD
and solve for D. Show your work
sin 2
mathematically and then place the formula for D in the box given.
D
10. Use the initial launch velocity
vo found in #7, the formula you found for D in #11, and your
scientific calculator to find the horizontal distance D the ball will travel for the following launch
angles of the catapult arm.
Launch Angle

Distance
D
5
15
25
35
45
55
65
75
85
11. Based off your calculations in the table above, what would be the best launch angle  for the
catapult arm if you want to get the ball to travel the maximum possible distance from the catapult?
12. If you set the catapult arm at this angle
 , how far will the ball land from the catapult?
13. Now you need to adjust the catapult base so the launch angle will give you a maximum distance.
You will need to change the launch angle from the initial launch angle found in #6 to the angle
 you determined would net the maximum distance for the ball, found in #13. Determine the
adjustment factor between your two angles and place your answer in the box. For example, if you
found the initial launch angle in #6 was
36 and the angle that would net the maximum distance in
#13 to be 52 then your catapult will need to be adjusted by 52  36  16 .
Adjustment Factor 
14. In order to launch the ball at the angle that will achieve the maximum distance, you will need to
create an angle with the floor and the catapult base by placing wooden blocks under the front of
the catapult. Carefully measure the angle between the catapult and the floor until you have raised
the base up to the adjustment factor found in the last step. Hold the catapult securely at the
correct angle. Fire the catapult and record the distance. This should be longer than for an
unadjusted launch. Record this distance.
Distance =
15. Suppose you want to launch the ball from the catapult to hit a target that lies at a point set at 2/3
of the maximum distance found above. Use the formula given below and your scientific calculator
to determine to determine the angle required to achieve this distance. Show all your work
mathematically in the space provided and then put your answer in the box provided.
1
 gD 
  sin 1  2 
2
 v0 

16. Set the catapult to launch at the angle determined for this distance. The catapult base will again
have to be adjusted to achieve this requirement. Place wooden blocks appropriately until you have
adjusted the launch angle to the proper degree measurement and hold securely at the correct
angle. Fire the catapult and record the distance. The distance should be close to desired.