A model rocket is projected straight upward from ground level according to the height equation h=-16t^2+120t

Question

A model rocket is projected straight upward from ground level according to the height equation h=-16t^2+120t, where h is the height of the rocket in feet and t is the time in seconds. What is the maximum height Of the rocket?

Answer 1

h(t) = -16t² + 120t

 

h_max occurs at the vertex of the height vs. time parabola, at

 

t = -120/[2(-16)] = 3.75 s

 

Evaluate h(t) at 3.75 s, and that will be the maximum height.

 

h_max = h(3.75) = -16(3.75)² + 120(3.75) = ? ft

 

You can finish from here.