Question

A quarter falls off a building that is 144

feet tall. If the equation for height as a

function of time is

h(t) = -16t2 + initial height where t is

time in seconds and h(t) is height in

feet, how many seconds will it take for

the quarter to hit the ground?

Answer 1

3 seconds

Explanation:

Initial height = 144 feet

t = Time taken

The equation of the height from the ground is

`h(t)=-16t^2+\text{Initial height}`

The time taken to reach the ground is needed. Here the ground is taken as reference so
`h(t)=0`

`0=-16t^2+144\\\Rightarrow -144=-16t^2\\\Rightarrow t=\sqrt{(144)/(16)}\\\Rightarrow t=3\ \text{s}`

So, time taken by the quarter to reach the ground is 3 seconds.