Page 108 - Calculus Demystified

CHAPTER 3 Applications of the Derivative
We now have a general formula (namely (†)) for the position of a falling body at 95
time t. [Recall that we were first introduced to this formula in Section 2.6.] See
Fig. 3.17.

Fig. 3.17

Before doing some examples, we observe that a falling body will have initial
velocity 0. Thus

0 = h (0) =−32 · 0 + v 0 .
Hence, for a falling body, v 0 = 0. In some problems we may give the body an
initial push, and then v 0 will not be zero.

EXAMPLE 3.14
Suppose that a falling body hits the ground with velocity −100 ft/sec. What
wasthe initial height of the body?

SOLUTION
With notation as developed above, we know that velocity is given by

h (t) =−32t + 0.
We have taken v 0 to be 0 because the body is a falling body; it had no initial
push. If T is the time at which the body hits the ground, then we know that

−100 = h (T ) =−32 · T.
As a result, T = 25/8 sec.