In a lake, a fish rising vertically to the surface of water uniformly at the rate of 3 m/s, observes a bird diving vertically towards the water at the rate of 9 m/s. The actual velocity of the dive of the bird is (given, refractive index of water =4/3)

Options

A. `4.5ms^(-1)`
B. `5.4ms^(-1)`
C. `3.0ms^(-1)`
D. `3.4ms^(-1)`

Answer

A

Explanation

Effective height of the bird as seen by the fish,
`Y=y+muy^(')`
`(dY)/(dt)=(dy)/(dt)+mu(dy^('))/(dt)`
`9=3+(4)/(3)(dy^('))/(dt)`
or `(dy^('))/(dt)=(6xx3)/(4)=(18)/(4)=(9)/(2)=4.5ms^(-1)`
Therefore, actual velocity of bird `=4.5ms^(-1)`