An arrow is projected into air. Its time of flight is $8 s$ and range is $200 m$ . What is the maximum height reached by it?
[Take $g = 10 {m s}^{- 2}$ ]

80 m

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24.5 m

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18.25 m

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46.75 m

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Solution

The correct option is A $80 m$
Given time of flight is:
$T = \frac{2 u sin θ}{g} = 8 s$ ... (1)
Given range of the arrow is:
$R = \frac{u^{2} sin 2 θ}{g} = 200 m$ ... (2)

Also, maximum height is given by:
$H = \frac{u^{2} {sin}^{2} (θ)}{2 g}$ ....(3)

From (1) and (3),
$H = \frac{T^{2} \times g}{8} = 80 m$

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