An aeroplne `A` is flying horizontally due east at a speed of `400 km//hr`.Passengers in `A`, observe another aeroplane `B` moving perpendicular to direction of motion of `A`.Aeroplane `B` is actually moving in a direction `30^(@)` north of east in the same horizontal plane as shown in the figure.Determine the velocity of `B`

Options

A. `400sqrt3hati+400sqrt3hatj`
B. `400hati+400/(sqrt(3))hatj`
C. `400hati+400hatj`
D. `400/sqrt3hati+400hatj`

Answer

B

Explanation

`vecV_(A)=400hati, vecV_(B)=v_(B) cos 30^(@) hati+v_(B) sin 30^(@) hatj`
`vecV_(B)=(v_(B)sqrt3)/2hati+v_(B)/2hatj,`
`vecV_(B//A)=vecV_(B)-vecV_(A)`
`vecV_(B)=(v_(B)sqrt3/2hati+v_(b)/2hatj)-400hati`
`vecV_(B//A)=(v_(B)sqrt3/2hati-400)hati+v_(B)/2hatj`
`sqrt3v_(B)-800=0,v_(B)=/800/sqrt3,vecV_(B)=400hati+400/sqrt3hatj`