Question

A rocket is launched in the air. Its height in feet is given by h, left bracket, t, right bracket, equals, minus, 16, t, squared, plus, 120, th(t)=−16t 2 +120t where tt represents the time in seconds after launch. What is the appropriate domain for this situation?

Answer 1

the appropriate domain for the function is [0, 7.5].

Explanation:

The rocket cannot be launched before time 0, so the domain must include 0. The rocket will eventually hit the ground, so the height cannot be positive forever. The maximum height of the rocket is reached when the derivative of the function is 0, which happens at t = 7.5 seconds. So the domain should include all values of t between 0 and 7.5 seconds.

Therefore, the appropriate domain for the function is [0, 7.5].