A man can go straight across a river in 5 min when the water flows at 10 m/s. How long will it take him to do the same if the water is still.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The man can go straight across a river in 5 minutes when the water flows at 10 m/s. To do this he would have to travel at an angle such that the component of his velocity in the direction opposite to that in which the water flows is equal to 10 m/s. If he travels at a velocity with magnitude V at an angle x to the line perpendicular to the sides, V*sin x = 10

`V^2*sin^2 x = 100` ...(1)

If the river is D m wide, `D/(V*cos x)` = 5 minutes

`D^2/25 = V^2*cos^2x` ...(2)

Adding (1) and (2)

`D^2/25 + 100 = V^2`

`V = sqrt(D^2/25 + 100)`

If the river is still, the person travels perpendicular to the bank and the time taken to cross the river is:

`D/V = D/sqrt(D^2/25 + 100)`

The time taken to cross the river is dependent on the width of the river and equal to `D/sqrt(D^2/25 + 100)` 

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