Question

A spaceship launched into the air has a height (feet) at any given time (seconds) as h=-t^2+10t until it hits the ground. At what time(s) is it at a height of 9 feet above the ground

Answer 1

The spaceship is at a height 9 feet above the ground at 1 second and 9 second after lunched.

Explanation:

Given that a spaceship launched into the air has a height at any time as

`h=-t^2+10t`

where h is height in feet and t is time in second.

To find the time when the height of the spaceship is 9, we need to put h=9 in the given equation.

`\therefore 9=-t^2+10t`

`\Rightarrow t^2-10t+9=0`

`\Rightarrow t^2-9t-t+9=0`

`\Rightarrow t(t-9)-1(t-9)=0`

`\Rightarrow (t-9)(t-1)=0`

`\Rightarrow t=1,9`

The spaceship is at a height 9 feet above the ground at 1 second and 9 second after lunched.