Two trains `A` and `B` are moving with same speed of `100km//hr`.Train `A` moves towards east and train `B` moves towards west.An an instant when the trains are moving side by side, an aeroplane files above the trains horizontally.For the passengers in the train `A`, the plane appears to fly from North to South direction.For the passengers in the train `B`, the plane appears to fly in a direction making an angle `60^(@)` to North-South direction.

Options

A. The speed of the plane with respect to ground is `100sqrt(7/3)km`
B. The speed of the plane with respect to ground is `100sqrt3km`
C. The plane moves in a direction at an angle of `"tan"^(-1)sqrt3/2` to North-South direction (with respect to ground)
D. The plane moves in a direction at an angle of `"tan"^(-1)sqrt5/2` to North-South direction (with respect to ground)

Answer

A, C

Explanation

`barv_(P)=ai+bj,barV_(A)=100i`
`barV_(PA)=(a-100)i+(b-100)j,a=100`,
`barv_(B)=-100i,barv_(P)=200i+bj`
`tan 60=200/B:B=200/sqrt3,barV_(P)=100i-200/sqrt3j`