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A Closer Look

Free Fall
here are two different meanings for the ward. The resisting force is determined by 130 mi/h). The air resistance increases with
Tterm free fall. In physics, free fall means at least two variables: (1) the area of the increased speed, and the net force becomes
the unconstrained motion of a body in a object exposed to the airstream and (2) the less and less. Eventually, the downward
gravitational field, without considering air speed of the falling object. Other variables weight force will be balanced by the upward
resistance. Without air resistance, all ob- such as streamlining, air temperature, and air resistance force, and the net force be-
jects are assumed to accelerate toward the turbulence play a role, but the greatest ef- comes zero. The person now falls at a con-
2
surface at 9.8 m/s . fect seems to be from exposed area and the stant speed, and we say the terminal velocity
In the sport of skydiving, free fall means increased resistance as speed increases. has been reached. It is possible to change
falling within the atmosphere without a A skydiver’s weight is constant, so the your body position to vary your rate of fall
drag-producing device such as a parachute. downward force is constant. Modern sky- up or down by 32 km/h (about 20 mi/h).
Air provides a resisting force that opposes divers typically free-fall from about 3,650 m However, by diving or “standing up” in free
the motion of a falling object, and the net (about 12,000 ft) above the ground until fall, experienced skydivers can reach speeds
force is the difference between the down- about 750 m (about 2,500 ft), where they of up to 290 km/h (about 180 mi/h). The re-
ward force (weight) and the upward force open their parachutes. After jumping from cord free fall speed, done without any special
of air resistance. The weight of the falling the plane, the diver at first accelerates equipment, is 517 km/h (about 321 mi/h).
object depends on the mass and accelera- toward the surface, reaching speeds up to Once the parachute opens, a descent rate of
tion from gravity, and this is the force down- about 185 to 210 km/h (about 115 to about 16 km/h (about 10 mi/h) is typical.

downward velocity is shown in Figure 2.16 as increasingly longer
velocity arrows (v v ). There are no forces in the horizontal direc-
tion if you can ignore air resistance, so the horizontal velocity of
the arrow remains the same, as shown by the v h velocity arrows.
The combination of the increasing vertical (v v ) motion and the
v = 0 unchanging horizontal (v h ) motion causes the arrow to follow a
curved path until it hits the ground.
An interesting prediction that can be made from the shot
arrow analysis is that an arrow shot horizontally from a bow
will hit the ground at the same time as a second arrow that is
simply dropped from the same height (Figure 2.16). Would this
be true of a bullet dropped at the same time as one fired hori-
zontally from a rifle? The answer is yes; both bullets would hit
the ground at the same time. Indeed, without air resistance, all
the bullets and arrows should hit the ground at the same time if
dropped or shot from the same height.
Golf balls, footballs, and baseballs are usually projected
upward at some angle to the horizon. The horizontal motion
of these projectiles is constant as before because there are no
horizontal forces involved. The vertical motion is the same
as that of a ball projected directly upward. The combination
of these two motions causes the projectile to follow a curved
path called a parabola, as shown in Figure 2.17. The next time
you have the opportunity, observe the path of a ball that has
v = max
been projected at some angle. Note that the second half of the
path is almost a reverse copy of the first half. If it were not
FIGURE 2.15 On its way up, a vertical projectile is slowed by for air resistance, the two values of the path would be exactly
the force of gravity until an instantaneous stop; then it accelerates the same. Also note the distance that the ball travels as com-
back to the surface, just as another ball does when dropped from
pared to the angle of projection. An angle of projection of
the same height. The straight up and down moving ball has been
moved to the side in the sketch so we can see more clearly what 45° results in the maximum distance of travel if air resistance
is happening. Note that the falling ball has the same speed in the is ignored and if the launch point and the landing are at the
opposite direction that it had on the way up. same elevation.

2-15 CHAPTER 2 Motion 39