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?

Question

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Respuesta :

belgrad belgrad · Answer 1 · 2020-06-20T15:55:48+02:00

Answer:

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

[tex]\frac{d h}{d t} = - 16 ( 2 t) + 128(1)[/tex] ...(ii)

Now equating Zero , we get

[tex]\frac{d h}{d t} = -32 t + 128 =0[/tex]

- 32 t =-128

t = 4

Step(ii):-

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

[tex]\frac{d^2 h}{d t^2} = -32 (1) <0[/tex]

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