Question

A ball is projected upward from ground level. After t seconds, it’s height in feet is a function defined by f (t) = -16t^2 + 96t. In how many seconds will the rocket be at a height of 128 ft above the ground?

Answer 1

t = 2 s and t = 4 s

Explanation:

A ball is projected upward from ground level. After t seconds, it’s height in feet is a function defined by,

`f (t) = -16t^2 + 96t`

We need to find in how many seconds will the rocket be at a height of 128 ft above the ground.

It means,

`128= -16t^2 + 96t\\\\-16t^2+96t-128=0\\\\16(-t^2+6t-8)=0\\\\(-t^2+6t-8)=0\\\\-t^2+4t+2t-8=0\\\\t(-t+4)-2(-t+4)=0\\\\(t-2)=0\ and\ (-t+4)=0\\\\t=2\ and\ t=4`

So, it will be at a height of 128 feet at 2 second and 4 second.