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  4. A man can swim with a speed of 4 km h-1 in still water. He crosses a river 1 km wide that flows steadily at 3 km h-1. If 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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Q. A man can swim with a speed of $4\,km\,h^{-1}$ in still water. He crosses a river $1\,km$ wide that flows steadily at $3\,km\,h^{-1}$. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?

Motion in a Plane

Solution:

Time to cross the river,
$t=\frac{\text{Width of river}}{\text{Speed of man}}$
$=\frac{1\,km}{4\,km\,h^{-1}}$
$=\frac{1}{4}h$
Distance moved along the river in time $t$,
$s=v_{r}\times t=3\,km\,h^{-1}\times\frac{1}{4}h=\frac{3}{4}km$
$=750\,m$