Page 55 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 4

Motion in a

Vertical Plane

ACCELERATION OF GRAVITY

All bodies in free fall near the earth’s surface have the same downward acceleration of
2
g = 9.8 m/s = 32 ft/s 2
A body falling from rest in a vacuum thus has a velocity of 32 ft/s at the end of the first second, 64 ft/s at the end
of the next second, and so forth. The farther the body falls, the faster it moves.
A body in free fall has the same downward acceleration whether it starts from rest or has an initial velocity
in some direction.
The presence of air affects the motion of falling bodies partly through buoyancy and partly through air
resistance. Thus two different objects falling in air from the same height will not, in general, reach the ground at
exactly the same time. Because air resistance increases with velocity, eventually a falling body reaches a terminal
velocity that depends on its mass, size, and shape, and it cannot fall any faster than that.

FALLING BODIES
When buoyancy and air resistance can be neglected, a falling body has the constant acceleration g, and the
formulas for uniformly accelerated motion apply. Thus a body dropped from rest has the velocity
v = gt
2
1
after time t, and since s = at , it has fallen through a vertical distance of
2
1
h = gt 2
2
From the latter formula we see that

2h
t =
g
and so the velocity of the body is related to the distance it has fallen by v = gt, or

v = 2gh
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