Question

2.On top of a hill, a rocket is launched from a distance 80 feet above the lake. The rocket will fall into the lake is given by the equation h=-16t²+64t+80, where t is time in seconds. What is the maximum height reached by the rocket?

Answer 1

Given : On top of a hill, a rocket is launched from a distance 80 feet above the lake. The rocket will fall into the lake is given by the equation h=-16t²+64t+80, where t is time in seconds.

To Find : What is the maximum height reached by the rocket?

Solution:

h=-16t²+64t+80

dh/dt  = -32t  + 64

dh/dt   = 0

=>  -32t  + 64  = 0

=> t = 2

d²h/dt²  = - 32 < 0

Hence height is maximum at t = 2

h=-16t²+64t+80

at t = 2

h = -16(2)²  + 64(2) + 80

= 144 feet

maximum height reached by the rocket  =   144 feet

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