Round numerical answers to the nearest hundredth, if necessary.

A water bottle rocket is shot upward with an initial velocity of vi = 40 ft/s from the roof of a school, which is at hi = 70 ft above the ground. The equation h = -

1

2

at2 + vit + hi models the rocket's height as a function of time. The acceleration due to gravity a is 32 ft/s2.

We are to find how long will it take to return to the ground?

Answer:

t = 0.48 sec

Step-by-step explanation:

We are given;

initial velocity; vi = 40 ft/s

hi = 70 ft

acceleration due to gravity; a = 32 ft/s²

Now, we are given that the rocket's height as a function of time is;

h = - 12at² + vit + hi

At ground, h = 0

Plugging in the relevant values to obtain;

0 = - 12 (32) t² + 40t + 70

-384t² + 40t + 70 = 0

The roots of the equation gives; t = 0.48 sec