a man can swim at a speed 2m/s in still water. he starts swimming in a river at an angle 150 to the direction of water flow and reaches the directly opposite direction on the opposite bank.
find the speed of flowing water.
if width of river is 1km then find time taken to cross the river

Dear Student,

it is the problem of shortest path to crosss a river.

Vector diagram shows that angle between spped of man and that of river is 150 

or, angle the man makes with the straight line joining the opposite sides of the river= 150-90=60

Thus, velocity component across this straight line= vcos60

​and velocity componenet acting opposite to that of velocity of river=vsin60

$$\begin{gathered} or v_{river}=2\times \frac{\sqrt{3}}{2} or, v_{river}=\sqrt{3} i.e 1.73 m/s \\ time taken to cross the river= \frac{S}{v\cos 60}=\frac{1000}{2\times 0.5}=1000 s or, 16.67 min \end{gathered}$$

Regards.