A fish rising vertically to the surface of water in a lake uniformly at the rate of 2 ~m / s observes a kingfisher diving vertically towards the water at a rate of 10 ~m / s . If refractive index of water n= 4 3 , what will be the actual velocity of the kingfisher

Step-by-step solution

Velocity of bird w.r.t. fish, v_ B F =10 ~m / s and velocity of fish w.r.t. ground V_ F G =2 ~m / s Distance between bird and fish, as seen by fish S=x+n y on differentiating w.r.t. time, we get aligned & d S d t = d x d t +n d y d t & v_ B F =v_ F G +n v_ B G & 10=2+ 4 3 v_ B G & v_ B G = 8 4 / 3 =6 ~m / s & aligned