Question

The height of a rocket is given by the equation h = −16t 2 + 2448t, where the height is measured in feet above the ground and the time, t, is measured in seconds. How long will it take for the rocket to hit the ground?

Answer 1

153 s

Explanation:

Given:

The variation of height of a rocket above ground with time 't' is given as:

`h=-16t^2+2448t`

In order to reach the ground, the height will be 0 feet.

So, plugging in 0 for 'h' and solving for time 't', we get:

`0=-16t^2+2448t\\\\16t^2=2448t\\\\16t^2-2448t=0\\\\16t(t-153)=0\\\\t=0\ s\ or\ t=153\ s`

So, at time
`t=0\ s`, the rocket is at the ground or it is its launch point. Then after 153 seconds, it will again reach the ground.

So, the time it take for the rocket to hit the ground is 153 s.