A swimmer crosses the river along the line making an angle of `45^@` with the direction of flow. Velocity of the river water is `5(m)/(s)`. Swimmer takes 12 seconds to cross the river of width 60 m. The velocity of the swimmer with respect to water will be:

Options

A. `10 m//s`
B. `5 m//s`
C. `5sqrt(5) m//s`
D. `5sqrt(2) m//s`

Answer

B

Explanation

Time taken by mean to cross the river
`= ("width of river")/(v_(y))12=(60)/(v_(y))`

`v_(y) = 5 m//sec`
Let the `x` component of velocity of man w.r.t. to river to `V_(x)`
Since velocity of man w.r.t. to ground makes an angle of `45^(@)` with river flow
`x` component of velocity of man w.r.t. to ground `v_(r) + v_(x) = V_(y)`
`5 + V_(x) = 5`
`V_(x) = 0`.
So velocity of man w.r.t to water `= v_(y) = 5 m//sec`.