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

Explanation

Here
`:. v_(A) = v_(B) cos 30(@)`
`:. 100 sqrt(3) = v_(B) xx (sqrt(3))/(2) `
`:. v_(B) = 200 ms^(-1)`
` Time = ( displacement)/( velocity)`
`:. t_(0) = (500) /( v_(B) sin 30(@)) = (500) /( 200xx sin 30(@ )) = 5 sec `