A man wishes to row across a river flowing to the right with speed of 2m/s. If they velocity that the boat can have `V_(B) = 4 m//s` , how should the man row so as to reach across in .
(a) shortest path (b) shortest time .

Explanation

(a) Shortest Path .
If the main has to move along the shortest path , then the path of this boat should be AB ( perpepndicular to river).
If the man rows vertically , the river will carry him to right , hence the man should incline his boat to the left. When his velocity is inclined , it has two components , `V_(x)` and `V_(y)` [compare with inclined velocity of cat].

The horizontal component `V_(x)` should cancel the speed the river .
Thus `V_(x) = V_(B) cos theta = V_(R)`
`therefore 4 cos theta =2 , theta = 60^(@)`
Alternatively , we can use resultant vertical as in cat mouse problem (Method 3).
(b) Shortest time :
Note that when the man rows along shortest distance , he DOES NOT cross the river in the shortest time , because time taken to cross the river ` = ("widthe of river")/("vertical velocity")`
As long as the boat is inclined at angle `theta` , vertical velocity is `V_(B)` . To row in shortest time , the enitre velocity of boat should be used in vertical direction i.e., Man should row perpendicular to stream .
Note : When the man rows in shortest time , he does not reach point B but instead point B. Shortest distance is analogus to reaching a point on opposite bank (say house ) where shortest time is linked with only reaching opposite bank.