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
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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):
   \[
   \theta = \arctan{\left(\frac{\text{opposite side}}{\text{adjacent side}}\right)}
   \]
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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