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At the same instant, two boys throw balls A and B from a window with speeds $v_{0}$ and $k v_{0}$ respectively, where k is constant. They collide in air at time t. which of the following options (s) is/are correct?

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$k = \frac{\sin θ_{2}}{\sin θ_{1}}$

$k = \frac{\cos θ_{2}}{\cos θ_{1}}$

$t = \frac{h}{(k v_{0} \sin θ_{1} + v_{0} \sin θ_{2})}$

$t = \frac{h}{(k v_{0} \cos θ_{1} + v_{0} \cos θ_{2})}$

answer is B, C.

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Detailed Solution

In x-direction;

$d = v_{0} \cos θ_{2} t = (k v_{0} \cos θ_{1})$ t

$k = \frac{\cos θ_{2}}{\cos θ_{1}}$

Motion of A w.r.t B in y-direction

$h = v_{r} t, v_{r} = (k v_{0} \sin θ_{1} + v_{2} \sin θ_{2})$

$t = \frac{h}{v_{r}} = \frac{g}{k v_{0} \sin θ_{1} + v_{0} \sin θ_{2}}$

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