A body is dropped from a height of 100m at what height the velocity of the body will be equal to one half of velocity when it hits the ground?

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45 m

65 m

55 m

75 m

answer is A.

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Detailed Solution

$\begin{array}{l} v = \sqrt{2 gh} = \sqrt{1960} \\ v_{1} = \frac{v}{2} = \frac{\sqrt{1960}}{2} \\ Now, {v_{1}}^{2} - u^{2} = 2 gh \\ \frac{1960}{4} - 0^{2} = 2 gh \\ \Rightarrow h = 25 m \\ ∴ 100 - 25 m = 75 m \end{array}$

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