Question

A ball is thrown from a point O aiming a target at angle 30⁰ with the horizontal, so that the ball hits the target at B but the ball hits at point A, a vertical distance h below B. If the initial velocity of the ball is 20 $m s^{- 1}$ and the horizontal distance between O and C is 10m. Find the value of h.

Moderate

Solution

In moving horizontal distance 10 m, the ball will fall by distance $\frac{1}{2} g t^{2} .$
$As, R = u \cos θ t$
$\Rightarrow 10 = 20 \times \cos 30 ° t = 20 \times \frac{\sqrt{3}}{2} t \Rightarrow t = \frac{1}{\sqrt{3}} s$
$y = A B = u \sin θ t - \frac{1}{2} g t^{2} = \frac{10}{\sqrt{3}} - \frac{g}{6} h e i g h t B C = 10 \tan 30 = \frac{10}{\sqrt{3}} s o h e i g h t A B = B C - A C = \frac{10}{\sqrt{3}} - \frac{10}{\sqrt{3}} + \frac{g}{6} = \frac{g}{6}$

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