Question

A ball is thrown from the ground to a wall 3 m high at a distance of 6 m . If the ball just clears the wall and falls 18 m away from the wall, the angle of projection of ball is

Moderate

Solution

Here, $R = \frac{u^{2} \sin 2 θ}{g} = 24$
$∵ y = x \tan θ - \frac{g x^{2}}{2 u^{2} \cos^{2} θ}$
$3 = 6 \tan θ - \frac{36 g}{2 u^{2} \cos^{2} θ}$ …(ii)
From Eq. (i), we get
$\frac{g}{u^{2}} = \frac{\sin 2 θ}{24} = \frac{\sin θ \cos θ}{12}$
Substituting in Eq. (ii), we get
$3 = 6 \tan θ - \frac{3}{2} \tan θ = \frac{9}{2} \tan θ \Rightarrow θ = \tan^{- 1} (\frac{2}{3})$

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