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  4. Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal as shown in figure. The speed of A is 100√3 ms-1. 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 is

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Q. Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^°$ and $60^°$ with respect to the horizontal as shown in figure. The speed of $A$ is $100\sqrt{3}\,ms^{-1}$. 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 $t = t_0$, $A$ just escapes being hit by $B$, $t_0$ isPhysics Question Image

Motion in a Plane

Solution:

The relative velocity of $B$ with respect to $A$ is perpendicular to the line of motion of $A$.
$\therefore v_{B}cos30^{°}=v_{A}$
$v_{B}=\frac{v_{A}}{cos\,30^{°}}$
$=\frac{100\sqrt{3}}{\sqrt{3}/2}200\,ms^{-1}$
$\therefore t_{0}=\frac{500}{v_{B}\,sin\,30^{\circ}}$
$=\frac{500}{200\times\frac{1}{2}}=5\,s$

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