In a river of 20 m width. Half part of river flows with speed `10 m//sec` and remaining half part flows with `20m//sec` as shown in figure. A man starts to swim from A and reaches to point B in 10 sec. Man swims with speed `V_m` with respect to river at an angle `theta` with line AB. Then, angle `theta` will be : (man swims with constant speed and in same direction with respect to river throughout the motion):

Options

A. `tan^(-1)(5)`
B. `tan^(-1)(15/2)`
C. `cos^(-1)(2/15)`
D. `tan^(-1)(1/5)`

Answer

B

Explanation

`10(V_(m) cos theta)=20`
`V_(m) cos theta=2m//sec`
`V_(m) sin theta=15 m//sec`
`tan theta=15/2`