Chapter 3, Problem 63P

(I) Huck Finn walks at a speed of 0.70m/s across his raft (that is, he walks perpendicular to the raft’s motion relative to the shore). The raft is traveling down the Mississippi River at a speed of 1.50 m/s relative to the river bank (Fig. 3-49). What is Huck’s velocity (speed and direction) relative to the river bank?

FIGURE 3-49

Problem 58.

58. Call the direction of the flow of the river the x direction, and the direction of Huck walking relative to the raft the y direction.

$\begin{array}{c}{\stackrel{\to }{v}}_{\text{Huck rel}\text{. bank }}={\stackrel{\to }{v}}_{\text{Huck rel}\text{. raft }}+{\stackrel{\to }{v}}_{\text{raft rel}\text{. bank }}=0.70\hat{j}\text{ m/s + 1}\text{.50}\hat{i}\text{ m/s}\\ \text{= }\left(1.50\hat{i}+0.70\hat{j}\right)\text{m/s}\end{array}$

$\text{Magnitude: }{v}_{\text{Huck rel}\text{. bank }}=\sqrt{{1.50}^2+{0.70}^2}=1.66\text{ m/s}$

$\text{Direction: }\theta {\text{=tan}}^{-\text{1}}\frac{0.70}{1.50}=25°\text{ relative to river}$