A man can row a boat at 4.0km/hr in still water. A river flows at 2.0km/hr. (a) if he is crossing the river, in what direction the oat shou ld go to reach a point directly opposite to his staring point? (b) if the river is 4.0km wide how long will it take him to cross the river? (c) How long will it take him to row 2.0km down the river and then back to his starting point? (d) How long will it take him to row 2.0 km up the river and then back to his starting point? (e) in what direction the boat shou ld go, if he wants to cross he river in teh smallest possible time?

Answer

(a `30^(@)` to vertical ; (b) `2//sqrt(3)` hr, (c) 4/3 hr, (d) 4/3 hr; (e) perpendicu lar to shore.

Explanation

`|vecV_(M//R)|=4.0` km/hr.
`|vecV_(R//G)|=2.0` km/hr
`sin theta=(2)/(4)=(1)/(2)`
`theta=30^(@)`
`t=(4.0)/(4 cos 30^(@))=(2)/sqrt(3)` hr
`d_("drift")=v_(R)xxt`

In order to cross the river in minimum time he shou ld go perpendicu lar to river flow.