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?

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?

anonymous · Answer

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.

anonymous · Answer

so you end up with an equation like this 0=-16t^2+144t-288??

anonymous · Answer

hi radar.

radar · Answer

You can simplify this and not need to use the quadratic.
$$288=-16t ^{2}+144t$$
Divide through by 16 getting 18=-t^2 + 9t

anonymous · Answer

so you end up with 3 and 6?

radar · Answer

$$t ^{2}-9t+18=0$$ Is what you would get after rearranging the equation  Now you have something you can easily factor.  Hi Raslk2kl1

radar · Answer

Yes now I don't know if that means it was above 288 feet for the time 3 thru 6 seconds or not.  can you figure that out

anonymous · Answer

Yes, the way I enter the answers seems like it is between 3 and 6 seconds

radar · Answer

Fine, good luck.