Question

Suppose an object is dropped from a height h0 above the ground. Then its height after t seconds is given by h = −16t 2 + h0, where h is measured in feet. Use this information to solve the problem.
A ball is dropped from the top of a building 59 ft tall. (Round your answers to three decimal places.)
(a) How long will it take to fall half the distance to ground level?
t = sec
(b) How long will it take to fall to ground level?
t = sec

Answer 1

Answer:

Step-by-step explanation:

Given

$h=-16t^2+h_0$

ball is dropped from a height of $59 ft$

therefore $h_0=59 ft$

$h=-16t^2+59$

Time taken to fall half the distance to the ground level i.e. $h=\frac{59}{2}$

$\frac{59}{2}=-16t^2+59$

arranging we get

$16t^2=\frac{59}{2}$

$t^2=\frac{59}{2\times 16}$

$t=1.35 s$

(b)Time taken to fall

i.e. h=0

$0=-16t^2+59$

$16t^2=59$

$t^2=\frac{59}{16}$

$t=1.92 s$