Vector Addition: Calculate Magnitude of Sum

[joej24]

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

 

[betel]

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.

 

[joej24]

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!

 

[betel]

Good.

 

[rwisz]

I would like to clarify and explain the concept of vector addition and how to calculate the magnitude of the sum. Vector addition is the process of combining two or more vectors to obtain a single vector, known as the resultant. The magnitude of the resultant is calculated using the Pythagorean theorem, as you correctly attempted. However, it is important to note that the magnitude of the resultant is not simply the sum of the magnitudes of the individual vectors.

In this case, the magnitude of the sum would be the square root of (20^2 + 25^2) = 32.0156. This means that the answer is not exactly 12, but rather a value close to it. Therefore, the correct answer is option C.

It is also important to mention that the direction of the resultant vector is determined by the direction of the individual vectors being added. This can be calculated using trigonometric functions such as sine and cosine.

In conclusion, when adding vectors, it is crucial to understand the concept of vector addition and how to calculate the magnitude and direction of the resultant. I hope this explanation helps in understanding the solution to this problem.