Chapter 3, Part 2
Free-Fall, Projectile Motion
Copyright © 2010 Pearson Education, Inc.
Freely Falling Objects
Objects falling in a
vacuum fall at the
same speed,
regardless of mass
Copyright © 2010 Pearson Education, Inc.
Freely Falling
Objects Accelerate
at a Rate of
–9.81 m/s2
Copyright © 2010 Pearson Education, Inc.
Free fall is the motion of an object subject
only to the influence of gravity. The
acceleration due to gravity is a constant, g.
Copyright © 2010 Pearson Education, Inc.
Motion with Constant Acceleration
v f = vi + at
1
vav = (vi + v f )
2
1
s = (vi + v f )t
2
1 2
s = vi t + at
2
2
2
(v f ) = (vi ) + 2as
Copyright © 2010 Pearson Education, Inc.
If I throw a ball straight upward at 12.0 m/s, what
will be its maximum height?
2
2
(v f ) = (vi ) + 2as
0 = 12.02 + 2(-9.81)s
s = 7.34 m
How long will it be airborne?
v f = vi + at
0 = 12.0 + (-9.81)t
t = 1.22 s
(twice this time is 2.44 s)
If I drop an egg from the roof of a building that is 90
meters tall, how long will it take to hit the ground?
1 2
s = vi t + at
2
Copyright © 2010 Pearson Education, Inc.
-90 = ½ (-9.81) t2
t = 4.28 s
Projectile Motion
Copyright © 2010 Pearson Education, Inc.
Projectile Motion
Copyright © 2010 Pearson Education, Inc.
Projectile Motion
The acceleration is independent of the direction
of the velocity
Copyright © 2010 Pearson Education, Inc.
Projectile Motion
The vertical and
horizontal
components of the
velocity
are independent
Copyright © 2010 Pearson Education, Inc.
The vertical component
determines how high the
projectile goes, and how
much time it spends in
the air.
vi
visin θ
The horizontal component
and the time airborne
determine how far the
projectile goes.
vicos θ
Copyright © 2010 Pearson Education, Inc.
Playing shortstop, you pick up a ground ball and throw it
to second base. The ball is thrown horizontally, with a
speed of 22m/s, directly toward point A. When the ball
reaches the second baseman 0.45 s later, it is caught at
point B. How far were you from the second baseman and
what is the distance of the vertical drop?
Copyright © 2010 Pearson Education, Inc.
v Solution
v vi = 22m/s
v t = 0.45s
1 2
s = vi t + at
2
Horizontal Component:
s = 22(0.45) + ½ (0) t2
s = 9.9 m
Vertical Component:
s = 0 + ½ (-9.81)(0.452)
s = -0.99 m
Copyright © 2010 Pearson Education, Inc.
A soccer ball is kicked with a speed of 9.50m/s
at an angle of 25.0° above the horizontal. If
the ball lands at the same level from which it
was kicked, how long was it in the air? How
far did it go?
Copyright © 2010 Pearson Education, Inc.
v Solution
The vertical component is visin θ
9.50 sin 25.0° = 4.01 m/s
v f = vi + at
0 = 4.0149 + (-9.81)t
t = 0.409 s
The total time is twice this.
2t = 2(0.409 s) = 0.818 s
The horizontal component is vicos θ
9.50 cos 25.0° = 8.61 m/s
1 2
s = vi t + at
2
Copyright © 2010 Pearson Education, Inc.
s = 8.61(0.818) + 0 = 7.04 m
Homework
p. 78
pp. 82-84
Copyright © 2010 Pearson Education, Inc.
Multiple Choice (11-21 odd)
Probs. 79, 89, 95, 103, 105, 109,
115, 119