a) The maximum height reached by the rocket = 331 ft
b) Time taken for the rocket to reach maximum height = 4.5 seconds
The maximum height is when the speed is 0m/s
That is, dh/dt = 0
[tex]h = -16t^2+144t+7[/tex]
Find dh/dt
[tex]\frac{dh}{dt} = -32t+144[/tex]
At maximum height, dh/dt = 0
0 = -32t + 144
32t = 144
t = 144/32
t = 4.5
The rocket reaches the maximum height after 4.5 seconds
Substitute t = 4.5 into h = -16t² + 144t + 7 to find the maximum height
h = -16(4.5²) + 144(4.5) + 7
h = -324 + 648 + 7
h = 331 feet
The maximum height reached by the rocket = 331 ft
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