Question

A swimmer’s speed in the direction of flow of a river is $16km{h^{ - 1}}$. Against the direction of the flow of the river, the swimmer’s speed is $8km{h^{ - 1}}$. Calculate the swimmer’s speed in still water and the velocity of the flow of the river.
A) $12km/h,4km/h$
B) $10km/h,3km/h$
C) $10km/h,4km/h$
D) $12km/h,3km/h$

Answer 1

Hint: Whenever two bodies or two particles interact with each other, in order to change their position, they apply force on each other. A force is basically a push or pull when two objects are interacting with each other.

Complete step by step answer:
Step I:
Given the upstream velocity of the swimmer against the river $ = 16km/hour$
The downstream velocity of the swimmer in the direction of the river $ = 8km/hour$
Let the velocity of the river is $ = a$
Also, suppose that the velocity of the swimmer is $ = b$
Step II:
As per the condition given in the question
When the swimmer is swimming in the direction of the flow of the river, then the swimmer’s hand will push the water in the backward direction. This will increase the speed of the swimmer.
$a + b = 16$ -----------(i)
When the swimmer is in the opposite direction to the flow of the river, then the velocity will decrease. Therefore
$a - b = 8$ -----------(ii)
Step III:
Solving equation (i) and (ii),
$\Rightarrow a + b = 16$
$\Rightarrow a - b = 8$
$\Rightarrow 2a = 24$
$\Rightarrow a = 12$
Step IV:
Substitute the value of ‘a’ in equation (i),
$\Rightarrow 12 + b = 16$
$\Rightarrow b = 4$

$\therefore$ The velocity of the river is $12km/hour$. The velocity of the swimmer is $4km/hour$. Hence, option A is the right answer.

Note:
It is to be noted that even though velocity and instantaneous velocity are the terms related to distance and displacement, they are different. Where velocity is the rate of change of displacement with time, the instantaneous velocity is the velocity of a particle at a given instant of time. If the velocity is not constant, then it will be different from the instantaneous velocity.