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Question:

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively. The speed of A is 100√3 m/s. At time t=0s, an observer in A finds B at a distance of 500m. 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:

5

8

6

7

Solution:

The relative velocity of B with respect to A is perpendicular to the line of motion of A.
∴VBcos30° = VA ⇒ VB = 200m/s
And time t0 = (Relative distance)/(Relative velocity) = 500/VBsin30° = 5sec