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Answer :
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket by evaluation is; 88 feet.
What is the maximum height reached by the rocket?
It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Ultimately, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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