LECTURE 7
PROJECTILE MOTION
Instructor: Kazumi Tolich
Lecture 7
2
¨ 
Reading chapter 3.4
¤  2-D
motions
¤  Projectile motions
n  x
and y components of a projectile motion
n  Zero launch angle
2D constant acceleration motion
3
¨ 
For a particle with an initial position (x0, y0), an
initial velocity (v0x, v0y), and a constant acceleration
(ax, ay), its equations of motion are given by:
Example: 1
4
¨ 
An object experiences a
constant acceleration of
2.00 m/s2 along the –x axis
for 2.70 s, attaining a
velocity of 16.0 m/s in a
direction 45° from the +x
axis. Calculate the initial
velocity vector of the object.
Example: 2
5
¨ 
Initially, a particle is moving at
4.10 m/s at an angle of 33.5°
above the horizontal. Two seconds
later, its velocity is 6.05 m/s at an
angle of 59.0° below horizontal.
What was the particle’s average
acceleration during these 2.00
seconds?
Projectile motion assumptions
6
The free-fall acceleration is constant over the range
of motion.
¨  The free-fall acceleration is directed downward.
¨  The rotation of Earth is ignored.
¨  The effect of air resistance is negligible.
¨ 
¤  This
assumption is often not justified, especially for high
velocity projectiles.
Projectile motion
7
In projectile motion, velocities in the x and y directions
are independent from each other.
¨  Constant velocity motion in the x direction.
¨  Constant acceleration motion in the y direction.
¨ 
Independent x- and y-components
8
Projectile motion: x component
9
¨ 
x component of a projectile is a constant velocity
motion.
ax (t ) = 0
vx (t ) = v0 x = v0 cosθ 0
v0
x (t ) = x0 + v0 x t
θ0
= x0 + v0 cosθ 0 t
Projectile motion: y component
10
¨ 
y component of a projectile is a constant acceleration
motion.
ay (t ) = −g
vy (t ) = v0 y + ay t
= v0 sin θ 0 − gt
1
y (t ) = y0 + v0 y t + ay t 2
2
1
= y0 + v0 sin θ 0 t − gt 2
2
vy2 ( Δy) = v02 y + 2ay Δy
= v02 sin 2 θ 0 − 2gΔy
v0
θ0
Clicker question: 1 & 2
11
Example: 3
12
¨ 
A diver runs horizontally off
the end of a diving board
with an initial speed
v0 = 1.75 m/s. If the diving
board is h = 3.00 m above
the water, what is the diver’s
speed just before she enters
the water?
Example: 4
13
¨ 
A swimmer runs horizontally off a
diving board with a speed of
v0 = 2.62 m/s and hits the water a
horizontal distance of d = 1.88 m
from the end of the board.
a) 
b) 
How high above the water was
the diving board?
If the swimmer runs off the
board with a reduced speed,
does it take more, less, or the
same time to reach the water?