The speed of a swimmer is 4 km/h in still water. If the swimmer makes his strokes normal to the flow of the river of wid

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

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Given: Speed of swimmer in still water is $4 \, \text{km/h}$ . River width is $1 \, \text{km}$ . Downstream drift is $750 \, \text{m} = 0.75 \, \text{km}$ .

Find: Speed of the river water.

River crossing diagram showing width 1 km or 1000 m, downstream drift x = 750 m, swimmer velocity normal to flow, river velocity horizontal, and resultant path slanting to the opposite bank.

Since the swimmer makes his strokes normal to the flow, his entire swimming speed is used to cross the river. Therefore, time taken to cross is

t = \frac{1 \, \text{km}}{4 \, \text{km/h}} = \frac{1}{4} \, \text{h}

The downstream drift is produced by the river current:

x = v_r t

Using $x = 0.75 \, \text{km}$ and $t = \frac{1}{4} \, \text{h}$ ,

0.75 = v_r \times \frac{1}{4}

v_r = 3 \, \text{km/h}

Therefore, the speed of the river water is $3 \, \text{km/h}$ .

Given: The swimmer moves perpendicular to the river flow with speed $4 \, \text{km/h}$ . The river width is $1 \, \text{km}$ , and the downstream displacement is $750 \, \text{m}$ .

Find: River speed.

Convert the drift into kilometres:

750 \, \text{m} = 0.75 \, \text{km}

Now calculate the crossing time from width and swimmer's speed:

t = \frac{\text{width}}{\text{speed of swimmer}} = \frac{1}{4} \, \text{h}

During this same time, the river carries the swimmer downstream by $0.75 \, \text{km}$ . Hence,

v_r = \frac{0.75}{1/4} = 3 \, \text{km/h}

So, the correct numerical answer is 3.

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