Answered: Find the magnitude and direction of the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Find the magnitude and direction of the velocity of a canoe on a river, measured with respect to the river, knowing that the canoe has a velocity of 0.6 m/s , 50 degrees south of east relative to the earth, and that the river is flowing at 0.7 m/s east relative to the earth. Express all the numbers in your final answer to two significant figures.

Expert Solution

Step 1

Equation for the velocity of canoe relative to earth is

$v_{C E} = v_{C R} + v_{R E}$

Consider east as positive x direction and south as positive y direction.

From above equation the velocity of canoe with respect to river is

$\begin{array}{rcl} v_{C R} & = & v_{C E} - v_{R E} \\ = & [(0.6 \frac{m}{s}) (\cos 50 i + \sin 50 j)] - [(0.7 \frac{m}{s}) i] \\ = & [0.38567 \frac{m}{s} i + 0.4596 \frac{m}{s} j] - [(0.7 \frac{m}{s}) i] \\ = & (- 0.31433 i + 0.4596 \frac{m}{s} j) \frac{m}{s} \end{array}$

Magnitude of the velocity of canoe with respect to river is

$\begin{array}{rcl} |v_{C R}| & = & \sqrt{{(0.31433 \frac{m}{s})}^{2} + {(0.4596 \frac{m}{s})}^{2}} \\ = & 0.5568 \frac{m}{s} \\ \approx & 0.56 \frac{m}{s} (2 sf) \end{array}$

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