A man can swim with a speed of 4.0 km h-1 in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km h-1 and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Asked by Krishna 15/12/2021 Last Modified 13 Apr

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A man can swim with a speed of 4.0 km h-1 in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km h-1 and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Asked by Krishna 15/12/2021 Last Modified 13 Apr

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Learn Chapter 4-Motion in a Plane

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Nazia Khanum · Accepted Answer

As an experienced tutor registered on UrbanPro, I'd be happy to help you with this problem.

To solve this question, we can use the concept of relative velocity. Let's break it down:

The man can swim at a speed of 4.0 km/h in still water.
The river flows at a speed of 3.0 km/h.
The width of the river is 1.0 km.

When the man swims across the river, he will need to compensate for the flow of the river. We need to find the resultant velocity, which is the vector sum of his swimming velocity and the river's flow velocity.

Let's denote:

vmanvman as the velocity of the man in still water (4.0 km/h),
vrivervriver as the velocity of the river flow (3.0 km/h), and
vresultantvresultant as the resultant velocity.

The resultant velocity (vresultantvresultant) can be found using the Pythagorean theorem because the man swims perpendicular to the river's flow:

vresultant=vman2+vriver2vresultant=vman2+vriver2

vresultant=(4.0 km/h)2+(3.0 km/h)2vresultant=(4.0km/h)2+(3.0km/h)2

vresultant=16.0+9.0vresultant=16.0+9.0

vresultant=25.0vresultant=25.0

vresultant=5.0 km/hvresultant=5.0km/h

So, the resultant velocity is 5.0 km/h.

Now, we can calculate the time taken to cross the river:

Time taken=DistanceSpeedTime taken=SpeedDistance

Time taken=1.0 km5.0 km/hTime taken=5.0km/h1.0km

Time taken=0.2 hoursTime taken=0.2hours

Now that we have the time taken, we can find out how far down the river he goes when he reaches the other bank. This can be calculated by multiplying the speed of the river by the time taken:

Distance down the river=River speed×Time takenDistance down the river=River speed×Time taken

Distance down the river=3.0 km/h×0.2 hoursDistance down the river=3.0km/h×0.2hours

Distance down the river=0.6 kmDistance down the river=0.6km

So, the man goes 0.6 km down the river when he reaches the other bank.

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A man can swim with a speed of 4.0 km h-1 in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km h-1 and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

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