Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 135 feet per second, then its height h after t seconds is given by the equation h(t) = -16t2 + 135t. How long will it take the rocket to return to the ground?

Answer 1

The toy rocket will return to the ground at 8.44 seconds

Explanation:

The height h of the toy rocket launched vertically as a function of the time t is given by:

`h(t)=-16t^2+135t`

The rocket will return to the ground when h=0:

`-16t^2+135t=0`

Factoring:

`t(-16t+135)=0`

There are two solutions:

t=0, t = 135/16 = 8.4375

The first solution corresponds to the moment the toy rocket was launched, the second is the time taken by the rocket to return to the ground.

The toy rocket will return to the ground at 8.44 seconds