You decide to walk from your home to your friend's house. He lives 164 meters away from you at an angle 59° South of East. What is the eastern component of your displacement? What is the southern component of your displacement?

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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You decide to walk from your home to your friend's house. He lives 164 meters away from you at an angle 59° South of East.

What is the eastern component of your displacement?
[______] m

What is the southern component of your displacement?
[______] m

Explanation: 

This question involves breaking down a vector into its components. The vector in this problem is the displacement from your home to your friend’s house. Since your friend lives 164 meters away at an angle of 59° South of East, you can use trigonometry to find the eastern and southern components of this displacement:

- **Eastern Component**: Use the cosine of the angle.
  - Eastern = 164 * cos(59°)

- **Southern Component**: Use the sine of the angle.
  - Southern = 164 * sin(59°)

The boxes are provided for calculating and entering the respective component distances in meters.
Transcribed Image Text:You decide to walk from your home to your friend's house. He lives 164 meters away from you at an angle 59° South of East. What is the eastern component of your displacement? [______] m What is the southern component of your displacement? [______] m Explanation: This question involves breaking down a vector into its components. The vector in this problem is the displacement from your home to your friend’s house. Since your friend lives 164 meters away at an angle of 59° South of East, you can use trigonometry to find the eastern and southern components of this displacement: - **Eastern Component**: Use the cosine of the angle. - Eastern = 164 * cos(59°) - **Southern Component**: Use the sine of the angle. - Southern = 164 * sin(59°) The boxes are provided for calculating and entering the respective component distances in meters.
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