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Two point objects one sliding down from rest on a frictionless inclined plane of inclination $β$ with the horizontal the other being projected in air from the point O at an angle $α$ with horizontal start their motion at the same instant. Initially both point objects are along the same vertical line. Both get to the point P at the same time and the same speed. Then choose the correct option(s).

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$\sin α = \frac{2}{\sin β}$

$2 \cos α = \cos β$

$\cos α = 2 \cos β$

$2 \sin α = \frac{1}{\sin β}$

answer is A, B.

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Detailed Solution

At the particles reach point P at same time, $\frac{2 v_{0} \sin α}{g} = \frac{v_{0}}{g \sin β} \Rightarrow 2 \sin α = \frac{1}{\sin β}$

Since their horizontal displacement are equal $v_{0} \cos α t = \frac{v_{0}}{2} t \cos β$

$2 \cos α = \cos β$

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