# A man can swim in still water with a speed of 3 m/s. #x# and #y# axes are drawn along and normal to the bank of the river flowing to right with a speed of 1 m/s. The man starts swimming from origin #O# at #t=0# second. Assume size ............?

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A man can swim in still water with a speed of 3 m/s. #x# and #y# axes are drawn along and normal to the bank of the river flowing to right with a speed of 1 m/s. The man starts swimming from origin #O# at #t=0# second. Assume size of man to be negligible. Find the equation of locus of all possible points where man can reach at #t=1 sec# ?

A man can swim in still water with a speed of 3 m/s.

##### 1 Answer

Suppose the swimmer swims with velocity

So the velocity components of the swimmer will be

and

As the river is flowing along

Net velocity along

These two velocities are independent on each other as they are orthogonal. The swimmer starts at origin

and

From [1] and [2] we get

So equation of locus of all possible points where man can reach at t=1sec will be