Chapter 8, Problem 57SGA

(a)

To determine

To Find: Theresultant velocity of the boat.

Answer to Problem 57SGA

  $13.7km/h$

Explanation of Solution

Given:A boat that travels $16km/h$ in a calm water is sailing along a current of $3km/h$ on a river $250m$ wide. The boat makes an angle of ${35}^{°}$ with the current heading into the current.

Using vectors for finding the resultant vector.

  $\begin{array}{l}\overrightarrow{b}=(16\cos {55}^{°})\overrightarrow{c}+(16\sin {55}^{°})\overrightarrow{j}\\ here\\ \overrightarrow{c}=-3\overrightarrow{j}\\ thus\\ \left|\overrightarrow{b}+\overrightarrow{c}\right|=\sqrt{{(16\cos {55}^{°})}^2+{(16\sin {55}^{°}-3)}^2}\\ \left|\overrightarrow{b}+\overrightarrow{c}\right|=13.7km/h\end{array}$

Hence, the resultant velocity is $13.7km/h$ .

(b)

To determine

To Find:How far upstream is the boat when it reaches to the other shore?

Answer to Problem 57SGA

  $275.3m$

Explanation of Solution

Given: A boat that travels $16km/h$ in a calm water is sailing along a current of $3km/h$ on a river $250m$ wide. The boat makes an angle of ${35}^{°}$ with the current heading into the current.

  $\begin{array}{l}\frac{u}{250}=\frac{16\sin {55}^{°}-3}{16\cos {55}^{°}}\\ u=250\left(\frac{16\sin {55}^{°}-3}{16\cos {55}^{°}}\right)\\ u=275.3m\end{array}$

Hence, the boat can go upstream $275.3m$ .