Question

A pine cone is 40 feet above the ground when it falls from a tree. The height h in feet of the pine cone above the ground can be modelled by h=-16t^2+40, where t is the time in seconds since the pine cone started to fall. Solve the equation for t. Write your answer in simplest form.

Answer 1

Explanation:

Given

height of the pine cone above the ground can be modelled by

`h=-16t^2+40`

When pine cone reaches the ground
`h=0`

`\Rightarrow 0=-16t^2+40`

`\Rightarrow 40=16t^2`

`\Rightarrow t=\sqrt{(40)/(16)}`

`\Rightarrow t=(√(40))/(4)`

`\Rightarrow t=(2√(10))/(4)`

`\Rightarrow t=(√(10))/(2)`

`\Rightarrow t=1.58\ s`

Thus cone take 1.58 s to reach ground