Chapter 3, Problem 37P

To determine

The Huck’s velocity relative to the river bank and the direction.

Answer to Problem 37P

The velocity of the Huck with respect to the bank is 1.8m/s and the direction is 19^o relative to the river.

Explanation of Solution

Given Data:

Finn walks at the speed of the 0.60m/s across his raft.

The raft is Mississippi river at the speed of 1.70m/s relative to the river bank.

The diagram is given as:

  

Calculation:

The velocity diagram is drawn as:

  

According to the law of the vectors:

  $\begin{array}{l}\overrightarrow{V_{HB}}=\overrightarrow{V_{HR}}+\overrightarrow{V_{RB}}\\ \text{where,}\\ \overrightarrow{V_{HB}}=\text{Velocity of Huck with respect to bank}\\ \overrightarrow{V_{RB}}=\text{Velocity of Huck with respect to bank}\\ \overrightarrow{V_{HR}}=\text{Velocity of Huck with respect to raft}\end{array}$

Now, the magnitude of the velocity of the Huck with respect to the bank:

  $\begin{array}{l}\left|\overrightarrow{V_{HB}}\right|=\sqrt{{\left(\overrightarrow{V_{HR}}\right)}^2+{\left(\overrightarrow{V_{RB}}\right)}^2}\\ =\sqrt{{0.60}^2+{1.70}^2}\\ =1.8\text{m/s}\end{array}$

Therefore, the velocity of the Huck with respect to the bank is 1.8m/s.

The direction is evaluated as:

  $\begin{array}{l}\theta ={\tan }^{-1}\left(\frac{V_{HR}}{V_{RB}}\right)\\ ={\tan }^{-1}\left(\frac{0.60}{1.7}\right)\\ ={19}^o\end{array}$