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Question: A man can swim with a speed of \(4 \mathrm {~km} \mathrm {~h} ^ { - 1 }\)in still water. He crosses ...

A man can swim with a speed of 4 km h−14 \mathrm {~km} \mathrm {~h} ^ { - 1 }in still water. He crosses a river 1 km wide that flows steadily at 3 km h−13 \mathrm {~km} \mathrm {~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?

A

500 m

B

600 m

C

750 m

D

850 m

Answer

750 m

Explanation

Solution

Time to cross the river,

t= Width of river  Speed of man \mathrm { t } = \frac { \text { Width of river } } { \text { Speed of man } }

=1km4kmh−1=14h= \frac { 1 k m } { 4 k m h ^ { - 1 } } = \frac { 1 } { 4 } h

Distance moved along the river in time t

=vr×t=3kmh−1×14 h=34 km=750 m= \mathrm { v } _ { \mathrm { r } } \times \mathrm { t } = 3 \mathrm { kmh } ^ { - 1 } \times \frac { 1 } { 4 } \mathrm {~h} = \frac { 3 } { 4 } \mathrm {~km} = 750 \mathrm {~m}