Question

A swimmer moving upstream passes a float at point P. After two hours, he returns and at this instant it meets the float again at a distance 15km from the point P. If the swimmer velocity in water remains constant, then find the speed of the river flow.

Answer 1

Hint: In order to find the solution to these kinds of questions apply the concept of relative motion. Relative motion is the measure of the motion of an object with respect to the other moving or stationary object. Relative velocity is defined as the vector difference between the velocities of the two bodies with respect to each other.
Formula Used:
${\text{Speed}} = \dfrac{{{\text{Distance}}}}{{{\text{time}}}}$

Complete step by step answer:
According to the question, while going downstream, the swimmer meets the float at a distance of 15km away from point P. Which means that in 2 hrs the float has travelled a distance of 15km along the direction of the water flow with the speed of the water.
Let us assume that the speed of the water is ‘v’.
Now, the speed of the river flow is given by
$v = \dfrac{{{\text{distance}}}}{{{\text{time}}}}$
Substituting the given values of the distance and time taken to complete the distance we get,
$ v = \dfrac{{15}}{2}$
$ \therefore v = 7.5kmh{r^{ - 1}}$
Thus, when the swimmer’s velocity in water remains constant, then the speed of the river flow is 7.5km/hr.
Hence, the speed of the river flow is 7.5km/hr.

Note:
The relative of an object is defined as the velocity of an object B in the rest frame of another object A. Mathematically, velocity of object B relative to object A is given as,
${\vec v_{ab}} = {\vec v_a} + \vec v{}_b$
All the motions are relative to some given frame of reference. For example, when a body is at rest which means that it is not in motion. This means that it is being described with respect to a frame of reference which is moving together with the body.