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 the figure. The speed of A is `100sqrt3 ms^(-1)`. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If a `t = t_0`, A just escapes being hit by B. `t_0` in seconds is

Answer

5

Explanation

For relative motion perpendicular to line of motion of `A`
`V_(A)=100 sqrt(2)=V_(B) Cos 30^(@)`
`V_(B)=100 m//s`
`t_(0)=(50)/(V_(B)sin 30^(@))=(500)/(200 xx(1)/(2))=5 sec`.