A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 128 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h equals negative 16 t squared plus 128 t plus 8h=−16t2+128t+8. How long will it take the rocket to reach its maximum height? What is the maximum height?

The rocket will be reach its maximum height at t= 4 seconds

The maximum height  'h' = 264 feet

Step-by-step explanation:

Step(i):-

Given the function 'h' = -16 t² + 128 t +8 ...(i)

Differentiating equation (i) with respective to 't' we get

...(ii)

Now equating Zero , we get

- 32 t =-128

      t = 4

Step(ii):-

Again Differentiating equation (ii) with respective to 't' we get

The maximum height at t= 4

The rocket will be reach its maximum height at t= 4 seconds

The maximum height  

                        h = -16 (4)² + 128 (4) +8

                              = 264

Conclusion:-

The rocket will be reach its maximum height at t= 4 seconds

The maximum height  'h' = 264

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answer: yes youre right.

step-by-step explanation: