Asked by Mitchell Balmas on Apr 25, 2024
Verified
What is the approximate sum of the following two vectors: magnitude 10 at 120° and magnitude 15 at 90°?
A) magnitude 20 at 210°
B) magnitude 23 at 30°
C) magnitude 24 at 102°
D) magnitude 27 at 210°
Vectors
Physical quantities characterized by having both magnitude and direction, commonly used in physics and engineering to describe forces, velocity, etc.
Magnitude
The size, extent, or importance of something, often used in mathematical contexts to describe the absolute value of quantities.
- Acquire an understanding of vector concepts, how vectors are represented, and the fundamentals of vector addition.
- Employ methods of vector addition to resolve issues concerning vector sums.
Verified Answer
MH
Marnie HarringtonApr 29, 2024
Final Answer :
C
Explanation :
To find the sum of two vectors, we convert their polar forms into rectangular coordinates (x = r*cos(θ), y = r*sin(θ)), sum the coordinates, then convert back to polar form. For the first vector: x1 = 10*cos(120°) = -5, y1 = 10*sin(120°) = 8.66. For the second vector: x2 = 15*cos(90°) = 0, y2 = 15*sin(90°) = 15. Summing these gives x = -5 + 0 = -5, y = 8.66 + 15 = 23.66. Converting back to polar form gives a magnitude of approximately 24 and an angle of arctan(23.66/-5) ≈ 102° (adjusted for the correct quadrant).
Learning Objectives
- Acquire an understanding of vector concepts, how vectors are represented, and the fundamentals of vector addition.
- Employ methods of vector addition to resolve issues concerning vector sums.