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A body projected at an angle of $α$ as angle of projection, just clears two walls, each of height a and separated by a distance 2a. Find the range

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$2 a \cot (\frac{2}{α})$

$a \cot (\frac{α}{2})$

$2 a \cot (\frac{α}{2})$

$a \cot (\frac{2}{α})$

answer is D.

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Detailed Solution

$y = x \tan α (1 - \frac{x}{R}) \begin{array}{l} a = x \tan α (1 - \frac{x}{R}) \\ a = (x + 2 a) \tan α [1 - (\frac{x + 2 a}{R})] \\ x = \frac{R - 2 a}{2} \\ \tan α R^{2} - 4 a R - 4 a^{2} \tan α = 0 \end{array}$

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