\[(a)\;\sin ^{-1} \frac{1}{2} \quad (b)\;\sin ^{-1} \frac{3}{4} \quad (c)\;\sin ^{-1} \frac{1}{3}\quad(d)\;\sin ^{-1} \frac{3}{5} \]

Taking X and Y direction as shown

$u_{Ax}=60 \cos 30 ^{\circ}$

$\qquad= 30 \sqrt 3 m/s$

$u_{Ay}=60 \sin 30=30 m/s $

$u_{Bx}=-50 \cos \alpha$

$u_{By}=50 \sin \alpha $

A and B reach the same height at same time condition for collision

$u_{Ay}=u_{By}$

$30=50 \sin \alpha$

$\alpha =\sin ^{-1} \bigg(\large\frac{3}{5}\bigg)$

Hence d is the correct answer.

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