A man can swim with a speed of 4.0 km h^{-1} ...

Motion in a Plane

Question : 13 of 32

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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?

Solution:

Speed of man,

v_x = 4

km h

^{-1}

Distance travelled = 1 km

Speed of river = 3 km h

^{-1}

If t = time taken to cross the river

Then,

t = \frac{\text{Distance}}{\text{Speed}}

= \frac{1\,\text{km}}{\frac{4\,\text{km}}{\text{h}^{-1}}} = \frac{1}{4}

hour

=15

minutes

The man is carried down by stream with velocity of river water.

∴ Distance travelled by man in 15

\text{min}\ \left( \text{or } \frac{1}{4}\,\text{h} \right)

= 3\,\text{km}\,\text{h}^{-1} \times \frac{1}{4}\,\text{h} = 750\,\text{m}

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