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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

A

3s

B

5s

C

2s

D

1s

Text Solution

Verified by Experts

The correct Answer is:
B
The relative velocity of B with respect to A is perpendicular to the line of motion of A.
`:.v_(B)cos30^(@)=v_(A)`
`v_(B)=(v_(A))/(cos30^(@))=(100sqrt(3))/(sqrt(3)//2)=200ms^(-1)`
`:.t_(0)=(500)/(v_(B)sin30^(@))=(500)/(200xx(1)/(2))=5s`
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