Chapter 9, Problem 111RE

To determine

To find: The distance downstream to which the swimmer will reach from the point directly across the river from the starting point.

Answer to Problem 111RE

The swimmer is $0.4\text{miles}$ away from the downstream and end up from the point directly across the river from the starting point

Explanation of Solution

Given:

The speed of the swimmer is $5$ miles per hour.

The speed of the current is $2$ miles per hour.

The width of the river is $1\text{mile}$ .

Calculation:

Consider the diagram for the given condition is shown in Figure 1

Figure 1

Here, the speed of the swimmer is $S_2$ , the speed of the river is $S_1$ and the speed of the Swiffer against the speed f the river is $S_3$ .

Then, by Pythagoras theorem, the hypotenuse is,

  $\begin{array}{l}{\left|\left|S_3\right|\right|}^2={\left|\left|S_1\right|\right|}^2+{\left|\left|S_2\right|\right|}^2\\ {\left|\left|S_3\right|\right|}^2=5^2+2^2\\ {\left|\left|S_3\right|\right|}^2=25+4\\ \left|\left|S_3\right|\right|=5.39\end{array}$

The time taken by the swimmer to swim across the river is,

  $\begin{array}{c}t=\frac{\text{1}}{\text{5}}\\ =0.2\text{hours}\end{array}$

The total distance covered by the swimmer from the point directly across the river is,

  $\begin{array}{c}d=2\times 0.2\\ =0.4\text{miles}\end{array}$

Thus, the swimmer is $0.4\text{miles}$ away from the downstream and end up from the point directly across the river from the starting point