Question

Allie fires a rocket from ground level. The height of the rocket is given by the formula h= 260t - 16t^2 (-16t squared), where t is the time in seconds after launch. How long will the rocket be in the air?

Answer 1

The rocket would be in the air for 8.125 seconds after launch.

Explanation:

Given that the height of the rocket, h = 260t - 16
`t^(2)`.

To determine how long the rocket would be in the air, differentiate h totally with respect to t.

So that, total derivative of h is given as;

`(dh)/(dt)` =
`(d(260t-16t^(2)) )/(dt)`

0 = 260 - 16 x 2t

= 260 - 32t

0 = 260 - 32t

32t = 260

t =
`(260)/(32)`

= 8.125

t= 8.125 seconds

The rocket would be in the air for 8.125 seconds after launch.