Chapter 6.3, Problem 39SSC

To determine

To explain:The navigation of boat in terms of the velocity relative to the water.

Answer to Problem 39SSC

The boat has to navigate with the velocity relative to the shore $\left(v_{\text{b/s}}\right)$ in order to reach the shore.

Explanation of Solution

Given:

The motion of a boat across a fast-moving river is shown below.

Consider the boat has to cross the river to reach the shore. The velocity of the boat relative to the flowing river denoted by $v_{\text{b/r}}$ is known. The velocity of the flowing river relative to the shore denoted by $v_{\text{r/s}}$ is known.

In order to reach the shore, the boat should move with a velocity relative to the shore $\left(v_{\text{b/s}}\right)$

The vector diagram showing the boat’s velocity is shown below.

From the vector diagram, the resultant of the velocity of water relative to the shore and the velocity of boat relative to the water gives the velocity of boat relative to the shore. The dotted lines show the velocity of the boat relative to the shore $\left(v_{\text{b/s}}\right)$ .Hence, the boat should move with the velocity $\left(v_{\text{b/s}}\right)$ in order to reach the shore.

Conclusion:

Thus, the boat has to navigate with the velocity relative to the shore $\left(v_{\text{b/s}}\right)$ in order to reach the shore.