Question

A projectile is fired straight up from ground level. After t seconds it's height is above the ground is h feet where h=-16t^2+144t. For what time period is the projectile at least 288 ft off the ground?

Answer 1

Plug in 288 for h, move it over to the right side and do the quadratic formula to solve for t. You will get 2 times, in between and including those times will give you the period it is at least 288 ft off the ground.

You can simplify this and not need to use the quadratic. 288=−16t^2+144t
Divide through by 16 getting
 18=-t^2 + 9t
t^2−9t+18=0 Is what you would get after rearranging the equation Now you have something you can easily factor

Answer 2

Answer:

3 sec or 6 sec.

Explanation:

Given that, from the ground level a projectile is fired.

The equation which is given after t sec is,

$h=-16t^{2} +144t$

The height of the projectile is given after t seconds is, $h=288 ft$

Now put this value in height equation will get.

$288=-16t^{2} +144t\\t^{2}-9t+18=0\\t^{2}-(6+3)t+18=0\\t^{2}-6t-3t+18=0\\t(t-6)-3(t-6)=0$

Therefore the value of t will be 3 sec or 6 sec when projectile is at least 288 ft off from the ground.