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

Answer:

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

Step-by-step 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.