The time taken to reaches its maximum height is 3s.
In the question,
It is given that,
Height, h(t) = [tex]96t - 16t^{2}[/tex]
The maximum value of the function is obtained if the first derivative of the function h (t) = 0.
[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]
⇒ [tex]t = 3[/tex]
So, time taken to reach its max height is 3 seconds.
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