Question

A person aiming to reach exactly opposite point on the bank of a atream is swimming with a speed of 0.5 m/sat an angle of 120 degree with a direction of flowof water.What is the speed of water in the stream?

Answer 1

Here Vr is the velocity of the river W.R.T ground , Vm is the velocity of man W.R.T ground , Vm is the velocity of man W.R.T river, V is the velocity of man W.R.T ground


                                 
                                           tan 90=Vm sin120/ Vr+Vm cos120
Vr= -Vm cos120=  -(0.5)(-0.5)= 0.25 m/s

Answer 2

Let the velocity of of  man be Vm and velocity of  flow of  water Vw as  shown in figure.

First  method:-

If  we  divide Vm in two components as  it  is  a vector  quantity, Then,

Horizontal component Vm.cos120° will be  equal to Vw,

Vm.cos120° = Vw

Vw =  Vm.cos120°

Vw = - 0.5 × 1/2

Vw = - 0.25

|Vw| = 0.25 m/s

Second  Method,

In ΔABC,

sin30° = AB/AC

1/2 = Vw/Vm

Vw = 0.5 × 1/2

Vw = 0.25 m//s