Projectile Motion
► All
objects move in air along a similar path.
Explain the shape of that path.
► What
is this curve called? (math class)
Projectile Motion
►PARABOLA
► Can
be represented mathematically
► Same
old stuff
Projectile Motion
Combining the Laws of Motion and what we
know about vectors, we can predict the
path of projectiles.
REMEMBER… X & Y COMPONENTS ARE
INDEPENDENT OF EACH OTHER!!!!!
Projectile Motion
► Projectile
– An object with independent
vertical (y) and horizontal (x) motions that
moves through the air only under the
influence of gravity after an initial thrust
► Trajectory
the air
– the path of a projectile through
Projectile Problem
You accidentally throw your car keys
horizontally at 9.0 m/s from a cliff 74 m
high. How far away from the base of the
cliff should you look for your keys?
X
Y
Projectile Problems
► Organize
information in terms of X and Y
components
X
Y
Projectile Problems
► Organize
information in terms of X and Y
components
X
Vx = 9.0 m/s
dx = ?
Y
Δdy = 74m
Projectile Problems
► What
information, that is not stated in the
problem, do we know.
X
Y
Vx = 9.0 m/s
Δdy = 74m
dx = ?
ay = 9.8 m/s2
vyi = 0 m/s  at peak of parabola
for 2nd half of the trip
Projectile Problems
► What
one variable is part of both the x and
y components?
TIME
► To solve for dx, we need the time
vx = d x / t
Projectile Problems
► Can’t
► Can
solve for t using the X components?
we solve for t using the Y?
YEP!
Projectile Problems
Y’s
Δdy = 74m
ay = 9.8 m/s2
vyi = 0 m/s  at peak of parabola
t=?
Use 2nd half of parabolic motion, where
vyi = 0 m/s (peak of parabola)
Δdy = vyit + ½ ayt2
Projectile Problems
► Solve
for t
dy = vit + ½ at2
74m = 0 + ½ (9.8m/s2) t2
Therefore,
t = √(74m / (½ (9.8m/s2) )
t = 3.9s
Projectile Problems
► Knowing
the time (3.9s) and vx (9.0m/s),
we can solve for dx (where we should look
for our keys)
► Using Vx = dx / t
9.0m/s = dx / 3.9s
dx = 35 m
We should look 35 m from the cliff
Projectile Motion Practice
Problem
►A
stone is thrown horizontally at a speed of
+5.0 m/s from the top of a cliff 78.4 m
high.
 How long does it take the stone to reach the
bottom of the cliff?
 How far from the base of the cliff does the
stone strike the ground?
 What are the horizontal and vertical
components of the velocity of the stone just
before it hits the ground?