The speed of a swimmer is 4 km h−14 km h-1 in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km1 km, he reaches a point 750 m750 m down the stream on the opposite bank. The speed of the river water is
Question
The speed of a swimmer is 4 km h−14 km h-1 in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km1 km, he reaches a point 750 m750 m down the stream on the opposite bank. The speed of the river water is
Solution
The problem can be solved by using the concept of relative velocity.
Step 1: Identify the given information
- The speed of the swimmer in still water (v_swimmer) = 4 km/h
- The width of the river (d) = 1 km
- The swimmer reaches a point 750 m down the stream on the opposite bank (d_downstream) = 0.75 km
Step 2: Calculate the time taken by the swimmer to cross the river The time taken by the swimmer to cross the river is the distance divided by the speed of the swimmer in still water. t = d / v_swimmer = 1 km / 4 km/h = 0.25 hours
Step 3: Calculate the speed of the river The speed of the river (v_river) is the distance downstream divided by the time taken to cross the river. v_river = d_downstream / t = 0.75 km / 0.25 hours = 3 km/h
So, the speed of the river water is 3 km/h.
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