A man can row a boat with 4 km/h in still water. If he is crossing a river where the current is 2 km/ (a) In what direction will his boat be headed it he wants to reach a point on the other bunk, directly oppos to starting point?(b) If width of the river is 4 km, how long will the man take to cross the river, with the condition in part (c) in what direction should he head the boat if he wants to cross the river in shortest time and what minimum time? is th(d) How long will it take him to row 2 km up the stream and then back to his starting point?

Explanation

(a)Given, that `v_(br)=4` km/h and `v_(r )=2` km/h
`therefore theta=sin^(-1)(v_(r ))/(v_(br))`
`=sin^(-1)(2/4)`
Hence, to reach the point directly opposite to starting point be should head the boat at an angle of `30^(@)` with or `90^(@)+30^(@)=120^(@)` with the river flow. (b) Time taken by the boatman to cross the river w-width of river = 4 km
`therefore v_(br)=4km/h` and `theta=30^(@)`
`therefore t= (4)/(4 cos 30^(@))=(2)/sqrt(3) h`
(c) For shortest time 80 and 1 Hence, he should head his boat perpendicular to the river current for crossing the river in shortest time and t shortest time is 1h.

or `t=(CD)/(v_(br)-V_(r ))+(DC)/(v_(br)+v_(r ))`
`=1+1/3=4/3h`