Add the following component vectors and determine the resultant. (You might want to draw them). Vector A = 35 m/s, south Vector B = 28 m/s, east O 45 m/s, 39 degrees east of south O 45 m/s, 51 degrees east of south O 7.9 m/s, 35 degrees east of north O 7.9 m/s, 22 degrees north of east
Add the following component vectors and determine the resultant. (You might want to draw them). Vector A = 35 m/s, south Vector B = 28 m/s, east O 45 m/s, 39 degrees east of south O 45 m/s, 51 degrees east of south O 7.9 m/s, 35 degrees east of north O 7.9 m/s, 22 degrees north of east
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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![**Vector Addition: Determine the Resultant Vector**
_Add the following component vectors and determine the resultant (You might want to draw them):_
**Vector A** = 35 m/s, south
**Vector B** = 28 m/s, east
**Options:**
- 45 m/s, 39 degrees east of south
- 45 m/s, 51 degrees east of south
- 7.9 m/s, 35 degrees east of north
- 7.9 m/s, 22 degrees north of east
**Explanation (If needed):**
To solve for the resultant vector, follow these steps:
1. Draw vectors A and B on a coordinate system based on the given directions.
2. Use the Pythagorean theorem to calculate the magnitude of the resultant vector (R), since vectors A and B are perpendicular to each other:
\[
R = \sqrt{(A^2 + B^2)}
\]
3. Find the direction of the resultant vector by using trigonometric functions, such as the tangent function to determine the angle θ relative to the east (or south):
\[
\theta = \arctan{\left(\frac{\text{opposite side}}{\text{adjacent side}}\right)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0a09bd-ef71-43b6-abcd-653755da1dfb%2F6ad27faa-622b-406c-832e-f84d3beae03e%2F38k526a_processed.png&w=3840&q=75)
Transcribed Image Text:**Vector Addition: Determine the Resultant Vector**
_Add the following component vectors and determine the resultant (You might want to draw them):_
**Vector A** = 35 m/s, south
**Vector B** = 28 m/s, east
**Options:**
- 45 m/s, 39 degrees east of south
- 45 m/s, 51 degrees east of south
- 7.9 m/s, 35 degrees east of north
- 7.9 m/s, 22 degrees north of east
**Explanation (If needed):**
To solve for the resultant vector, follow these steps:
1. Draw vectors A and B on a coordinate system based on the given directions.
2. Use the Pythagorean theorem to calculate the magnitude of the resultant vector (R), since vectors A and B are perpendicular to each other:
\[
R = \sqrt{(A^2 + B^2)}
\]
3. Find the direction of the resultant vector by using trigonometric functions, such as the tangent function to determine the angle θ relative to the east (or south):
\[
\theta = \arctan{\left(\frac{\text{opposite side}}{\text{adjacent side}}\right)}
\]
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