Question

The speed of a swimmer is $4 km h ^{-1}$ in still water If the swimmer makes his strokes normal to the flow of river of width $1 km$, he reaches a point $750 m$ down the stream on the opposite bank.The speed of the river water is ___ $km h ^{-1}$

Hint:

The swimmer’s drift is due to the velocity of the river current, and the time taken to cross the river is determined by the swimmer’s speed in still water.

Answer 1

Correct Answer: 3

The correct answer is 3

time to cross the River width $\omega =1000m$
$\text{is}=\frac{1km}{4km/h}$
Drift $x=Vm/g\times t$
Where $Vm/g$ is velocity of River w.r. to ground.
$x=Vm/g\times \frac{1}{4}=750m=\frac{3}{4}km$
$Vm/g=3km/hr$

Answer 2

The time to cross the river is given by: \[ \omega = 1000 \, \text{m} = 1 \, \text{km}, \quad v_s = 4 \, \text{km/h} \] The drift of the swimmer \( x \) is given by: \[ x = \frac{v_m}{g} \times t \] where \( v_m \) is the velocity of the river water with respect to the ground, and \( g \) is the acceleration due to gravity. From the geometry, we have: \[ x = 750 \, \text{m} = 0.75 \, \text{km} \] Substituting \( x = 750 \, \text{m} \) and the speed of the swimmer \( v_s = 4 \, \text{km/h} \), we can find \( v_m \): \[ x = \frac{v_m}{4} \times t \] Thus, \[ v_m = 3 \, \text{km/h} \]