A body is projected vertically upward from the top of a tower and it reaches the ground after 8 sec. When the same body is projected from the top of the same tower in vertically downward direction with same speed, it reaches the ground after 4 seconds. Then velocity of projection is

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20 m/s

25 m/s

15 m/s

10 m/s

answer is C.

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Detailed Solution

In the first case

$h = - u t_{1} + \frac{1}{2} g t_{1}^{2} ..... (1)$

Here upward physical quantities are considered negative and downward physical quantities are considered positive

$h = u t_{2} + \frac{1}{2} g t_{2}^{2} .......... (2)$

(2) - (1) $\Rightarrow u (t_{2} + t_{1}) + \frac{1}{2} g (t_{2}^{2} - t_{1}^{2}) = 0$

$\Rightarrow u = \frac{1}{2} g (t_{1} - t_{2}) = \frac{1}{2} \times 10 \times (8 - 4) m / s = 20 m / s$

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