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A stone is thrown vertically upwards and the height reached by it in time $t$ is given by $S = 80 t - 16 t^{2}$ then the stone reaches the maximum height in time $t$ = _____sec

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answer is 2.5.

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Detailed Solution

$S = 80 t - 16 t^{2}$

$\frac{d s}{d t} = 80 - 32 t$

At maximum height

$\frac{d s}{d t} = 0 \Rightarrow 32 t = 80 ∴ t = \frac{5}{2}$

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