A river is flowing from west to east at alphaspeed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river by the shortest path . Calculate the direction in which he should swim.

A river is flowing from west to east at alphaspeed of 5 metre per minu

1.	A river is flowing from west to east at alphaspeed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river by the shortest path . Calculate the direction in which he should swim.
Answer» Solution :The situation is shown in FIG. OA=A, represents velocity of river which is `5m mt^(-1)` OB=B , represents velocity of man in still water which is `10m mt^(-1)` The man starts swimming from O and goes along OB toreach C by shortest possible path . Here ,` /_AOC= beta =90^(@)` Here, `A=5 m mt^(-1), B=10m mt^(-1) beta = 90^(@),THETA=?` From formula , `tan beta = (B sin theta )/(A+B cos theta)` putting values, we get ,` tan90^(@)=(10 sin theta)/(5+10 cos theta)=oo (infinite)` Hence, `5+10 cos theta =0 or 10 cos theta = -5 ` (or) `cos theta =-0.5= cos 120^(@) i.e., theta = 120^(@)` It makes `/_COB=30^(@)` The man should swim along OB which is `30^(@) ` west of north .