Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t2 + 120t. How long will it take the rocket to return to the ground?

A) 7.5 seconds
B) 16 seconds
C) 3.75 seconds
D) 120 seconds

Answer 1

A) 7.5 seconds

Explanation:

Height of the ground is zero

-16t^2 + 120t = 0

Divide both sides by 16

-t^2 + 7.5t = 0

Factor out t

t(-t + 7.5) = 0

From the zero product rule

t = {0, 7.5}

0 would be time of launch

7.5 is time back to the ground