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Applications of Horizontal and Vertical Components

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Question

A ball is projected from the point O with velocity 20 m/s at an angle of $60^{\circ}$ with horizontal as shown in figure. At highest point of its trajectory it strikes a smooth plane of inclination $30^{\circ}$ at point A. The collision is perfectly inelastic. The maximum height from the ground attained by the ball is $\frac{75}{k}$ meter. Find the value of k? (g = 10 $m / s^{2}$ ) ___

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Solution

$H = \frac{20^{2} s i n^{2} 60^{\circ}}{2 g} = \frac{60}{4}$

$\frac{1}{2} m (5 \sqrt{3})^{2} = m (ω) h \Rightarrow h = \frac{15}{4}$
Max Height $= \frac{60}{4} + \frac{15}{4} = \frac{75}{4}$
$\Rightarrow k = 4$

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