Question

A person reaches a point directly opposite on the bank of a flowing river, while swimming at a speed of 5 m/s at an angle of 120° with the flow. the speed of the flow must be (a) 2.5m/s (b) 3m/s (c) 4m/s (d) 1.5m/s

Answer 1

Speed of swimmer=5m/s
Cos =B/H
Cos60=1/2
1/2=x/5
2x=5
X=2.5m/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 = - 5 × 1/2

Vw = - 2.5

|Vw| = 2.5 m/s

Second  Method,

In ΔABC,

sin30° = AB/AC

1/2 = Vw/Vm

Vw = 5 × 1/2

Vw = 2.5 m//s