Answered: You walk 33 m to the north, then turn…

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

You walk 33 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you originally started?

Expert Solution

Step 1

Let's assume $X$ -axis along the east direction and $Y$ -axis along north direction. Take, east and north as the positive $X$ and $Y$ direction respectively.

Let's draw a diagrammatic representation for the given problem.

In the above figure you walk first $33 m$ in the $A \to B$ then make a $60^{\circ}$ turn with the $Y$ -axis (north) towards the east and walk another $45 m$ from $B \to C$ .

Now the angle made by you with the $X$ -axis is

$θ = 90^{\circ} - 60^{\circ} = 30^{\circ}$

We need to find the magnitude of displacement, $|\vec{A C}|$ .

Now vector, $\vec{A B} = (0 m) \hat{i} + (33 m) \hat{j}$ where $\hat{i}$ is the unit vector along the $X$ -axis or eastward and $\hat{j}$ is the unit vector along the $Y$ -axis or northward.

Vector, $\vec{B C} = B C \cos (θ) \hat{i} + B C \sin (θ) \hat{j}$ where $B C$ is the magnitude of the vector $\vec{B C}$

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