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Answer :
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
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