Question

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

Answer 1

Hint: The man will drift in the direction of river current. Try to get time taken to cross the river. Use the formula $speed = \dfrac{{distance}}{{time}}$.

Complete step-by-step answer:

Let the velocity of river flow be ${V_R}$,
So, ${V_R} = 3km/hr$
Since the swimmer drive the boat normal to the flow of water, therefore time taken by the swimmer to cross the river is $t$,
$t = \dfrac{{dis\tan ce}}{{speed}} = \dfrac{{river\,width}}{{speed\,of\,man}}$
Here, width of river $ = d = 1km$
Speed of man in still water $ = {V_m} = 4km/hr$
Then, we get
$t = \dfrac{d}{{{V_m}}}$
Substitute the value of $d$and ${V_m}$ in above equation, so
 $
  t = \dfrac{d}{{{V_m}}} = \dfrac{{1km}}{{4km/hr}} \\
  t = \dfrac{1}{4}hr = 15\min \\
 $
Now due to speed of river flow, man drifts some distance from his normal direction on the other bank of the river in the direction of current flow, so in time $t$ the swimmer will also go down by distance $l$ due to river current.
Therefore, $l = $speed of river flow $ \times $ time taken to cross river
$l = {V_R} \times t$
Substitute the value of ${V_R}$ and $t$ in above equation
We get,
$
  l = \left( {3km/hr} \right) \times \left( {\dfrac{1}{4}hr} \right) \\
  l = \dfrac{3}{4}km = 0 \cdot 75km \\
  l = 750m \\
 $
Hence, the distance drifts by man due to current flow or the distance by which man goes down the river, when he reaches on another bank is $750m$.

Note: A man can swim with a certain speed, in still water to cross a river to a point directly opposite to the starting point in time to. When the river flows, he crosses the river directly along the same path in time.