Physics/Math Problem?

Question

A Ball projected vertically upward from the top of a tower has height (in feet) h(t)=-16t^2 + 64t + 80 after t seconds. At what time will the ball hit the ground?

Answer 1

The ball hits the ground when its height is 0.

h(t) = 0
-16t^2 + 64t + 80 = 0

Can divide by -16 to simplify:

t^2 - 4t - 5 = 0
(t-5)(t+1) = 0

t = 5 or t = -1.

Only positive answers are meaningful, so the ball hits the ground at 5 seconds.

Answer 2

0 = -16tt + 64t + 80.

Use the quadratic formula.