Question

# 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 figure. The speed of A is ( 100 sqrt{3} mathrm{ms}^{-1} ). At time ( mathrm{t}=0 mathrm{s} ), an observer in A finds ( B ) at a distance of ( 500 mathrm{m} ). This observer sees ( B ) moving with a constant velocity perpendicular to the line of motion of A. If at ( t=t_{0}, ) A just escapes being hit by ( B, t_{0} ) in seconds is.

Solution

( tan 30^{circ}=frac{d}{v_{A} t_{0}} )

( Rightarrow frac{1}{sqrt{3}}=frac{500}{100 sqrt{3 t_{0}}} quad t_{0}=5 s )