JEE Advance - Physics (2014 - Paper 1 Offline - No. 1)
Airplanes A and B are flying with constant velocity in the same vertical plane at angles $$30^\circ $$ and $$60^\circ $$ with
respect to the horizontal respectively as shown in the figure. The speed of A is $$100\sqrt 3 $$ m/s. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity
perpendicular to the line of motion of A. If at t = t0, A just escapes being hit by B, t0 in seconds is
Answer
5
Explanation
Since A observes B as moving normal to it
$${v_B}\cos 30^\circ = {v_A}$$
$${v_B}{{\sqrt 3 } \over 2} = 100\sqrt 3 $$
$${v_B} = 200$$ m/s
Therefore, $${t_0} = {{500} \over {200\sin 30^\circ }} = 5$$ s
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