Airplanes \( A \) and \( B \) are flying with constant velocity in the same vertical plane at an...

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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
\( \mathrm{P} \) horizontal respectively as shown in the figure. The speed of

W \( A \) is \( 100 \sqrt{3} \mathrm{~ms}^{-1} \). At time \( t=0 \mathrm{~s} \), an observer in \( A \) finds \( B \) at a distance of \( 500 \mathrm{~m} \). 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
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