Question
A ball is dropped from a height of $$20\,m$$ above the surface of water in a lake. The refractive index of water is $$4.3.$$ A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $$12.8\,m$$ above the water surface, the fish sees the speed of ball as
A ball is dropped from a height of $$20\,m$$ above the surface of water in a lake. The refractive index of water is $$4.3.$$ A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $$12.8\,m$$ above the water surface, the fish sees the speed of ball as
[Take $$g = 10\,m/{s^2}.$$
A.
$$9\,m/s$$
B.
$$12\,m/s$$
C.
$$16\,m/s$$
D.
$$21.33\,m/s$$
Answer :
$$16\,m/s$$
Solution :
Consider the activity $$A$$ to $$B,$$
Applying $${v^2} - {u^2} = 2as$$
$$\eqalign{ & {v^2} - {0^2} = 2 \times 10 \times 7.2 \cr & \Rightarrow v = 12\,m/s \cr} $$
The velocity of ball as perceived by fish is
$$v'{ = _w}\mu \times v = \frac{4}{3} \times 12 = 16\,m/s$$
Consider the activity $$A$$ to $$B,$$
Applying $${v^2} - {u^2} = 2as$$
$$\eqalign{ & {v^2} - {0^2} = 2 \times 10 \times 7.2 \cr & \Rightarrow v = 12\,m/s \cr} $$
The velocity of ball as perceived by fish is
$$v'{ = _w}\mu \times v = \frac{4}{3} \times 12 = 16\,m/s$$
