Question

A swimmer wishes to reach directly opposite bank of a river, flowing with velocity 8 m/s. The swimmer can swim 10 m/s in still water. The width of the river is 480 m. Time taken by him to do so:

• A. 60 sec
• B. 48 sec
• C. 80 sec
• D. none.

Answer 1

The correct option is C 80 sec

so to reach directly opposite bank of river he has to swim at an angle where component of his velocity cancel out the flow of water so that he can go directly opposite bank of the river.

so if we assume he is swimming at an angle $\theta$ with the flow, we get

$10Cos\theta =8$

and also $10Sin\theta$ will be component which will help him cross the river.

so if $Cos\theta =0.8$ then $Sin\theta =0.6$

velocity helping in crossing the river $=10\times 0.6=6m/s$

also distance is given $width=480m$

time taken will be $t=\frac{480}{6}=80$

so best answer is option C.