Question

A battalion of soldiers is ordered to swim across a river 500ft wide. At what minimum rate should they swim perpendicular to river flow in order to avoid being washed away by the waterfall 300ft downstream? The speed of current being 3m.p.h.
A. 6 m.p.h.
B. 5 m.p.h.
C. 4 m.p.h.
D. 2 m.p.h.

Answer 1

Hint: Due to flow of river the soldiers are drifted 300ft downstream which means we need to calculate the time taken by the soldiers to cover this downstream drift using the formula of
$\text{time}=\dfrac{\text{distance}}{\text{speed}}$
Using this value of time calculated above, we can calculate the rate i.e. the velocity at which the soldiers will cross the river of 500 ft width.

Complete step by step solution:
To avoid being washed by the waterfall of 300ft downstream, the time taken to cover it is given by
${{\text{t}}_{1}}=\dfrac{{{\text{d}}_{1}}}{{{\text{v}}_{1}}}$
Here, distance to be covered; ${{\text{d}}_{1}}$ = 300 ft.
${{\text{v}}_{1}}$= 3m.p.h (Speed of the current of water)
So the time taken is given by
${{\text{t}}_{1}}=\dfrac{300}{3}$
 = 100 sec
Now, distance to be travelled by the soldiers to cross the river is;
${{\text{d}}_{2}}$ = 500ft
Time taken to cross the river; ${{\text{t}}_{1}}$ = 100sec
Rate at which soldiers should swim in order to cross the river and not get drifted by the downstream flow of water;
$\text{v}=\dfrac{{{\text{d}}_{2}}}{{{t}_{1}}}$
 $\text{v}=\dfrac{500}{100}$
$v=5\text{ m}\text{.p}\text{.h}\text{.}$
Option (B) is the correct answer.

Note: Due to the speed of water flow (current) in the river, the soldier either swimming or floating stationary in the river experiences a pushing force along the flow direction (downstream). This push is called the drift.
The drift of the soldiers due to downstream flow of waterfall means that the soldiers should increase their speed rate as compared to the speed of current.