A river is following from west to east at a speed of 5m/minute. A boy on the south bank of the river, capable of swimming at 10 meters/minute in still water, wants to swin across the river in the shortest time, (i) Find the direaction in which he should swin, (ii) find the direction when drift along the river is zero.

Explanation

Along shortest path (AB).
The man will the river along the along the shortest path if the resultant of `vecv_2and vecv_1` is along AB.
` :. Sin theta = (v_2)/(v_1) =5/10 =1/2 = sin30^@`
`:. theta = 30^@ ` west of north.
(ii)
In shortest time :
Time ` = d/v_1 = d/(v cos phi)`
Time will be minimum if `cos phi` is maximum i.e . `phi = 0 `
The man should swin along AB i.e perpendicular to the flow .