Projectile Motion
Initial velocity is at an
angle  with respect to
the horizontal.
The only force on the
projectile is the
downward gravitational
force of Earth on the
projectile.

Path
Example
If you toss a ball horizontally in the +x direction,
sketch the path of the projectile.
Example
While standing on a 10-m high-dive, you throw a
ball downward at an angle of 30 from the
horizontal. Sketch the path of the ball.
x-component of motion
y-component of motion
Velocity components vx and vy

A ball is rolled horizontally off a
table. Assume air resistance is
negligible. Then between the
instant the ball leaves the table
and the instant it strikes the
floor, _________
A. vx = 0 and vy is constant but ≠ 0.
B. vx and vy are both constant but ≠ 0.
C. vx is constant but ≠ 0 and vy is increasing in magnitude.
D. vx is constant but ≠ 0 and vy is decreasing in magnitude.
E. vx and vy are both increasing in magnitude.
Acceleration components ax and ay

A ball is rolled horizontally off a
table. Assume air resistance is
negligible. Then between the
instant the ball leaves the table
and the instant it strikes the
floor, _________
A. ax = 0 and ay is constant but ≠ 0.
B. ax and ay are both constant but ≠ 0.
C. ax is constant but ≠ 0 and ay is increasing in magnitude.
D. ax is constant but ≠ 0 and ay is decreasing in magnitude.
E. ax and ay are both increasing in magnitude.
Note: Each answer has
a part for each blank.
With negligible air resistance, the thrown ball follows the path
traced in red. As it does so, the velocity of the shadow that it casts
on the wall ________ and the velocity of the shadow that it casts on
the ground __________.
A. becomes more positive and then less positive … doesn’t change
B. changes sign … doesn’t change
C. becomes more positive and then less positive … becomes more
positive and then less positive
D. changes sign … becomes more positive and then less positive
+
2
1
3
+x
With negligible air resistance, the thrown ball follows the
path traced in red. In the coordinate frame shown, the
ball’s acceleration is __________.
A. negative at points 1, 2, and 3
B. negative at point 1, zero at point 2, and positive at point 3
C. positive at point 1, zero at point 2, and negative at point 3
D. positive at points 1 and 3, but zero at point 2
E. negative at points 1 and 3, but zero at point 2
v0

A test rocket, due to technical failure,
experiences no further thrust from the
instant it leaves its ground level
launching pad until it lands on the
ground some distance away.
a. During its flight, the rocket’s horizontal position x __________
each time the clock advances by one second (Dt = 1 s).
A.
changes by the same positive amount
B.
changes by the same negative amount
C.
remains unchanged
D.
increases when the rocket is going up and
decreases when it is coming back down
v0

A test rocket, due to technical failure,
experiences no further thrust from the
instant it leaves its ground level
launching pad until it lands on the
ground some distance away.
b. During its flight, the rocket’s vertical position y __________
each time the clock advances by one second (Dt = 1 s).
A.
changes by the same positive amount
B.
changes by the same negative amount
C.
remains unchanged
D.
increases when the rocket is going up and
decreases when it is coming back down
v0

A test rocket, due to technical failure,
experiences no further thrust from the
instant it leaves its ground level
launching pad until it lands on the
ground some distance away.
c. During its flight, the rocket’s horizontal velocity component vx
__________ each time the clock advances by one second (Dt = 1 s).
A.
changes by the same positive amount
B.
changes by the same negative amount
C.
remains unchanged
D.
increases when the rocket is going up and
decreases when it is coming back down
v0

A test rocket, due to technical failure,
experiences no further thrust from the
instant it leaves its ground level
launching pad until it lands on the
ground some distance away.
d. During its flight, the rocket’s vertical velocity component vy
__________ each time the clock advances by one second (Dt = 1 s).
A.
changes by the same positive amount
B.
changes by the same negative amount
C.
remains unchanged
D.
increases when the rocket is going up and
decreases when it is coming back down
v0

A test rocket, due to technical failure,
experiences no further thrust from the
instant it leaves its ground level
launching pad until it lands on the
ground some distance away.
e. At the highest point in it’s trajectory, the rocket’s
velocity _____________ .
A. is zero
B. is horizontal
C. is vertical
D. has both a horizontal and a vertical component
.2
x in meters
1.
8
78.4
73.5
58.8
34.3
0
20
22.3
28
35.6
44
40
30
Series 1
Series 1
x
Series 1 Series 1
vx in m/s
y
vy in m/s
40
30
20
10
0
y in meters
y in meters
0
90
-9.8
80
-19.6
70
60
-29.4
50
-39.2
50
40
20
80
30
20
100
20
20
120
10
20
140
0
20
160
-10 0
4
-20
-30
-40
-50
90
0 20 40 60 80 10 12 14 16
80
t0in seconds
0
0
0
180
70
160
60
x in meters
140
50
120
40
100
30
80
20
60
10
40
0
0 1 2 3 4 20
5 6 7 8
0
20
10
0
The graph above shows the path of a projectile that is
unaffected by air resistance. The values of _______
are both different at point 1 than at point 2.
0
A. y and vy
B. x and vx
C. x and v
D. x and vy
E. ay and x
0
5
10
4
.2
x in meters
1.
8
78.4
73.5
58.8
34.3
0
20
22.3
28
35.6
44
40
30
Series 1
Series 1
x
Series 1 Series 1
vx in m/s
y
vy in m/s
40
30
20
10
0
y in meters
y in meters
0
90
-9.8
80
-19.6
70
60
-29.4
50
-39.2
50
40
20
80
30
20
100
20
20
120
10
20
140
0
20
160
-10 0
4
-20
-30
-40
-50
90
0 20 40 60 80 10 12 14 16
80
t0in seconds
0
0
0
180
70
160
60
x in meters
140
50
120
40
100
30
80
20
60
10
40
0
0 1 2 3 4 20
5 6 7 8
0
20
10
0
The graph above shows the path of a projectile that is
unaffected by air resistance. The quantities _______
both have the same values at point 1 that they do at
point 2.
A. y and vy
0
B. x and vx
C. ay and v
D. ay and vy
E. ax and x
0
5
10
4
Equations of Motion
Useful derived equations
Range
Useful derived equations
Peak height
Useful derived equations
time of flight
Example
A child swings on a playground swing and jumps off when the
swing has a velocity of magnitude 5 m/s at an angle of 40 and she
is 1 m off the ground. (a) What is her peak height and (b) where
does she land?
Example
The world record shot put is 23.12 m by American Randy Barnes in
1990. If the shot left his hand at a height of 1.5 m and an angle of
45, what was the shot’s initial speed?