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Question

If a rocket achieves a height expressed as h = 120t - 10t^2 after the initial upward launch where h= height in feet and t = time in second, what is the maximum height the rocket reaches? AND After how many seconds wil the rocket reach the ground?

Answer 1

you know your initial velocity is zero. you know your height. you know the acceleration due to gravity is 32.2 ft.sec^2. you know it's a one dimensional problem. I don't recall the kinematics formulas but i know you can solve any kinematics equation with just 3 known values. Also assume air resistance can be ignored

Answer 2

differentiate the height eq to determine t @ hmax:

dh/dt = 120-20t → t = 6 when dh/dt = 0

Ergo,

hmax = 120*6 - 10*6² = 360

Since the flight time equals twice the time required to reach hmax,

T = 2t = 12 sec