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

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=(59)/(2)`

`(59)/(2)=-16t^2+59`

arranging we get

`16t^2=(59)/(2)`

`t^2=(59)/(2* 16)`

`t=1.35 s`

(b)Time taken to fall

i.e. h=0

`0=-16t^2+59`

`16t^2=59`

`t^2=(59)/(16)`

`t=1.92 s`