Q)A river is flowing due east with a speed of 2 metre per second. A swimmer on the south bank of river can swim in still water at 4 metre per second. Swimmer swims in such a way that he reaches a directly opposite point on a North Bank. The result and speed of the swimmer is
a)5 m/s
b)2√3 m/s
c)3√2 m/s
d)4 m/s
Answers
The result and speed of the swimmer is 2√3 m/s
A river is flowing due east with a speed of 2 metre per second. A swimmer on the south bank of river can swim in still water at 4 metre per second. Swimmer swims in such a way that he reaches a directly opposite point on a North Bank.
Given,
The speed of the river = vr = 2 m/s
Velocity of the swimmer = vs = 4 m/s
As the swimmer starts swimming due south, then y-component of his resultant velocity is 4 m/s (south) and x-component (produced by river flow) is 2 m/s (east). Swimmer swims in such a way that he reaches a directly opposite point on a North Bank.
Therefore the swimmer's resultant velocity will be given by,
v = √ (vs² - vr²)
v = √ (4² - 2²)
v = √ ( 16 - 4 )
v = √12
∴ v = 2√3 m/s
The result and speed of the swimmer is 2√3 m/s
Option (b) is correct.