AP Physics 1: Projectile Motion Activity
Name _______________________________ Period ________
A ball is thrown from ground level with an initial velocity vo = 30.0 m/s. In the space below, sketch one example vector diagram with
components, determine the general equations you will use to calculate the components, and show one full sample calculation with  =
15o. After determining the general equations, calculate the initial vertical velocity (voy) and horizontal velocity components and fill in
the table below for each of the given angles (measured from the horizontal).
vo
General Equations:
vix = ____________________
viy = ____________________
(Record to two decimal places)
Angle
v0x (m/s)
v0y (m/s)
15.0o
30.0o
45.0 o
60.0 o
75.0o
90.0 o
Now you will simulate the motion of the ball. Open the GeoGebra simulation at: http://www.geogebratube.org/student/m167259 . The
ball is located at the origin, the units of the axes are meters, and the magnitude of the acceleration due to gravity is set to 9.80 m/s2. Set
the initial velocity of the ball to 30.0 m/s and the angle to 15.0 o. Hit the “Fire” button. Watch the ball as it moves through the air and
returns to the same level at which it started. Click the pause button. Use the time slider at the bottom of the simulation and the “singlestep” buttons to examine the motion. Look at the numerical readouts of horizontal and vertical position and velocity. Record in the
table below the total time the ball was in the air (find the point on the way down where the ball’s y height is closest to zero), The total
horizontal distance traveled (the x position at the time you just found), and the maximum height attained (find the point where vy is
closest to zero). Repeat this procedure for each of the six angles.
(Record to 3 significant figures)
Angle
15.0o
30.0o
45.0 o
60.0 o
75.0 o
90.0 o
Time in air
(s)
Horizontal
range (m)
Maximum
height (m)
Questions:
1) Which angle kept the ball in the air for the greatest time? _________
2) Which component of the initial velocity was related to the total time in air?
(horizontal, vertical, both)
3) Which angle took the ball to the greatest maximum height? ________
4) Which component of the initial velocity was related to the maximum height?
(horizontal, vertical, both)
5) At which angle did the ball attain maximum horizontal range? _______
6) Which component of the initial velocity was related to the horizontal range?
(horizontal, vertical, both)
7) Which two pairs of angles had identical horizontal ranges? 1) _____ and _____
2) _____ and _____
Do you notice anything the two pairs have in common? _________________________________________
8) What happens to the horizontal component of the velocity as the ball moves through the air? Explain why this
happens.
______________________________________________________________________________________________
______________________________________________________________________________________________
9) What happens to the vertical component of the velocity as the ball moves through the air? Explain why this happens.
______________________________________________________________________________________________
_____________________________________________________________________________________________
10) What is the vertical velocity of the ball at the point it reaches a maximum height?
_________________________________________________________________________
11) At what point is a projectile’s total speed a minimum?
_________________________________________________________________________
12) A projectile is launched at an initial velocity of 68 m/s with a horizontal angle of 76°. Use the simulation to answer
these questions:
a. What is its range? _________
b. Give another angle that will produce the same range: ______. Does the simulation verify your prediction?
c. What is the sum of the two angles that produce this range ____________
Now use the computer to create simulations to answer the following questions:
1) A ball is thrown at a 40.0o angle from the horizontal over level ground with an initial velocity of 28.0 m/s. a) What is the total
time the ball is in the air? b) How far does the ball travel before striking the ground? c) Find the time in air for a ball launched
with twice the initial velocity (56.0 m/s). d) What is the horizontal range of the faster ball? e) How many times farther
horizontally did the faster ball go?
Simulation Answers:
a)__________
b) __________
c) __________
d) ___________ e) _____________
Mathematical Solutions
2) A ball is thrown horizontally at 22.0 m/s from the top of a building 28.0 m high. a) How much time passes before the ball strikes
the ground? b) How far from the base of the building does the ball land? c) How much time would it take to strike the ground if
the ball was thrown horizontally with twice the initial velocity (44.0 m/s)? d) How far would the faster ball land from the base of
the building? e) How many times farther horizontally did the faster ball go?
Simulation Answers:
a)__________
b) __________
c) __________
Mathematical Solutions
d) ___________ e) _____________
3) A ball is thrown from the top of a cliff 95.0 m high with an initial speed of 30.0 m/s. It is thrown at an angle 45.0o above the
horizontal. a) How far does it travel horizontally before striking the ground? b) Repeat for a ball thrown at a 40.0o angle. c)
Which ball went farther before striking the ground?
Simulation Answers:
a)________________
b) ________________
Mathematical Solutions
c) __________________