Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^{\c

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 $t=0 \mathrm{~s}$, 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 $t=t_0, A$ just escapes being hit by $B, t_0$ in seconds is

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(b) : The relative velocity of $B$ with respect to $A$ is perpendicular to the line of motion of $A$. $\  	herefore \quad v_B \cos 30^{\circ}=v_A $ \  $ \begin{aligned} & v_B=\frac{v_A}{\cos 30^{\circ}}=\frac{100 \sqrt{3}}{\sqrt{3} / 2}=200 \mathrm{~m} \mathrm{~s}^{-1} \ & 	herefore \quad t_0=\frac{500}{v_B \sin 30^{\circ}}=\frac{500}{200 	imes \frac{1}{2}}=5 \mathrm{~s} \end{aligned} $