Answer to Question #20501 in Calculus for Riley

Question

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 16t^ + 32t, where s is in feet. How long {to the nearest tenth) will it take the
ball to fall 87 feet?

Answer 1

Let's consider the following equation:

16t² + 32t = 87,

or

16t² + 32t - 87 = 0.

This is a quadratic equation and its solutions are

t1 = ( -32 + √(32²+4*16*87) ) / (2*16) ≈ 1.5 [s]

and

t2 = ( -32 - √(32²+4*16*87) ) / (2*16) ≈ -3.5 [s].

The value of t2 is negative, therefore we discard it. So, it takes about 1.5 seconds the
ball to fall 87 feet.