Mirror is moving towards the particle with speed 2 cm/sec. Speed of A ad B are `10sqrt(2)` and 5 cm/sec respectively in the direction shown in figure. Magnitude of velocity of image of the particle B with respect to image of A.

Options

A. `sqrt(325)cm//sec`
B. `15cm//sec`
C. `13cm//sec`
D. `sqrt(269)cm//sec`

Answer

A

Explanation

Velocity of image of particle B
`overline(V)_(B)=5(hati)+4(-hati)=hati`
velocity of image of particle A
`V_(A)=10(-hati)+4(-hati)-10hatj`
`=14(-hati)-10hatj`
Relative velocity of image
`overline(V)_(BA)=overline(V)_(B)-overline(V)_(A)=hati-[14(-hati)-10hatj]=15hati+10hatj`
`|overline(V)_(BA)|=sqrt(325)cm//sec`