A ball is projected vertically upward from the ground. The ball is at the same height at t = 3 s and t = 9 s. The height of ball at t = 5 s is (g = 10 $m s^{- 2}$ )

175 m

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120 m

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135 m

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200 m

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Solution

The correct option is A $175 m$
The time of flight will be $t_{1} + t_{2} = 3 + 9 = 12 s$
but should be given by $T = \frac{2 u}{g}$ so $u = T g / 2 = \frac{12 \times 10}{2} = 60 m / s$
so the height at t=5second will be $h = u t - \frac{1}{2} g t^{2} = 60 (5) - \frac{1}{2} 10 (5)^{2} = 175 m$

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