Chapter 3, Problem 46P

To determine

The speed of river.

Answer to Problem 46P

367.1 m/s

Explanation of Solution

Given:

  $\begin{array}{l}\text{Velocity of boat, }{v}_B=1.70\text{ m/s}\\ \text{Drift, }d=110\text{ m}\\ \text{Width of river, }w=260\text{ m}\end{array}$

Formula Used:

  $\begin{array}{l}\text{Time take =}\frac{\text{Width of River}}{\text{Velocity}}\\ t=\frac{w}{v\sin \theta }\\ \text{Drift = time × Velocity along x-axis}\end{array}$

Calculation:

Substituting the value

  $\begin{array}{l}t=\frac{110}{1.70\times \sin 45°}\\ t=\frac{110\times \sqrt{2}}{1.70\times 1}\\ t=216.2\text{ sec}\end{array}$

Consider the given situation.

  

Substituting the value

  $\begin{array}{l}110=216.2-\left[v_B\cos 45-v_R\right]\\ 110=216.2-\left[260\cos 45-v_R\right]\\ v_R=367.1\text{ m/s}\end{array}$

Conclusion:

The speed of the river is 367.1 m/s.