Vector Addition: Calculate Magnitude of Sum

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Homework Help Overview

The problem involves the addition of two vectors with magnitudes of 20 and 25, and participants are exploring the possible magnitudes of their resultant vector. The context is vector addition, specifically focusing on how different orientations of the vectors affect the resultant magnitude.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss using the Pythagorean theorem to calculate the resultant magnitude and consider different orientations of the vectors to determine maximum and minimum possible magnitudes.

Discussion Status

Some participants have provided insights into the maximum and minimum magnitudes based on vector orientation, suggesting a range for the resultant magnitude. There is an acknowledgment of different approaches to the problem, but no explicit consensus on the final answer.

Contextual Notes

Participants are working within the constraints of the problem's multiple-choice format, which influences their reasoning about the possible magnitudes of the resultant vector.

joej24
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Homework Statement


A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
a. zero
b. 3
c. 12
d. 47
e. 50


Homework Equations


c ^2 = a^2 + b^2


The Attempt at a Solution



I was not entirely sure on what to do. I tried using the Pythagorean theorem to find the resultant of the 2 vectors and got 32. ( c ^2 = 20^2 + 25^2).
The answer by the way is C.

Thanks!
Joe
 
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Try do add the vectors in different ways. Then you will get a possible maximal and a minimal value for the magnitude of the resulting vector. All but one possible answers are outside of this region.
 
okay. I got it. The max magnitude of their addition would be when they are parallel in the same direction. mag would = 45. The min would be when they are parallel in the opposite direction. mag would = 5. Therefore the answer is 12. Thanks!
 
Good.
 

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