Chapter 9.6, Problem 6P

To determine

Tofind:the rate of swimmer in still water and the equation that flows.

Answer to Problem 6P

The rate of swimmer is $\text{2}\text{.5}\text{m}/\text{sec}$ .

Explanation of Solution

Given:

  $\text{r}$ is rate in $\text{km}/\text{h}$

  $\text{c}$ is rate in $\text{km}/\text{h}$

Travelling against the current rate:

  $\text{1}\text{.5}\text{m}/\text{sec}$ .

Traveling with current rate:

  $\text{3}\text{.5}\text{m}/\text{sec}$ .

Concept used:

If the thing is going against the gravity is taken as $\text{-ive}$ .

Vector formula:

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{+2ABcosθ}$ .

If the direction of any against the gravity means it make ${\text{180}}^0$ with the gravity.

  ${\text{R}}^2{\text{=A}}^{\text{2}}{\text{+B}}^{\text{2}}\text{-2AB}$ .

  $\text{R=A-B}$ .

  $\text{distance=rate}\times \text{time}$ .

Calculation:

Travelling against the current rate:

  $\text{1}\text{.5}\text{m}/\text{sec}$ .

Travelling against the current rateis given by $\text{r-c}$ .

  $\text{r-c=1}\text{.5}$ ………… $\left(\text{i}\right)$ .

Traveling with current rate:

  $\text{3}\text{.5}\text{m}/\text{sec}$ .

Traveling with the current rate is given by $\text{r+c}$ .

  $\text{r+c=3}\text{.5}$ …………… $\left(\text{ii}\right)$

Adding the equation $\left(\text{i}\right)$ and $\left(\text{ii}\right)$ :

  $\text{2r=5}$

Diving both side by $2$ :

  $\text{r=2}\text{.5}$ .

Substituting the value $\text{r=11}$ in equation $\left(\text{ii}\right)$ :

  $\text{r+c=3}\text{.5}$ .

  $\text{2}\text{.5+c=3}\text{.5}$ .

  $\text{c=1}\text{.}$

Hence, the rate of swimmer is $\text{2}\text{.5}\text{m}/\text{sec}$ .