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Airplanes A and B are flying with consta...

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 as shown in figure . The speed of `A` is `100sqrt(3) m//s` . At time `t = 0 s`, an observer in `A` finds `B` at a distance of `500 m`. The 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)` , A just escapes being hit by `B , t_(0)` in seconds is

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The correct Answer is:
5
For relative motion perpendicular to line of motion of A

`V_A = 100sqrt(3) = V_(B)cos 30^@ rArr V_(B) = 200 m//s`
`t_0 = 500/(V_(B)sin30^@) = 500/(200 xx 1/2) = 5 sec`.
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