Question

A model rocket is launched from the top of a tower 160 feet above the ground. The height "h" of the rocket "t" seconds after launch is given by the

function h (t) = -16t^2 +48t + 160. How long will it take the rocket to reach the ground after it has been launched?
5 seconds
4.5 seconds
2 seconds
6 seconds

Answer 1

(a) 5 seconds

Explanation:

You want to know the hang time of a model rocket launched at 48 ft/s upward from a height of 160 ft.

Time

The time it takes for the rocket to hit the ground is the positive solution to the equation ...

h(t) = 0

Filling in the expression for h(t), this is ...

-16t² +48t +160 = 0

t² -3t -10 = 0 . . . . . . . . . divide by -16

(t -5)(t +2) = 0 . . . . . . . . factor

The solutions make the factors zero: t = 5, t = -2. We want the positive solution: t = 5.

The rocket will take 5 seconds to reach the ground.