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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

Text Solution

Verified by Experts

The correct Answer is:
5

As observed from A, B moves perpendicular to line of motion of A.
It means velocity of b along A is equal to velocity of a
`V_(B) cos 30=100sqrt(3)`
`V_(B)=200`
If a is observer a remains stationary therefore
`t=500/(V_(B) sin 30)=500/100=5`
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