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 76 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

\[h = h_o/2 = -16*t^2+h_o \]\
thus
[(h_0/32)^(1/2)=t\]

for part a

Answer 2

a. t = (h_0/32)^(1/2)
b. t = (h_0/16)^(1/2)

Answer 3

rearranging equation gives
t=sqr ( [-h +h0] / 16 )

ergo
(a) t = 1.541
(b) t = 2.179

Answer 4

a. t = (h_0/32)^(1/2) b. t = (h_0/16)^(1/2)