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An aeroplne A is flying horizontally due...

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`

A

`400sqrt3hati+400sqrt3hatj`

B

`400hati+400/(sqrt(3))hatj`

C

`400hati+400hatj`

D

`400/sqrt3hati+400hatj`

Text Solution

Verified by Experts

The correct Answer is:
B
`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`
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Knowledge Check

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