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

Physics

Carson Liu

23 July, 23:09

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?

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Brayden Thompson · 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=-16 t^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