Is There More Than One Way to Solve a Trivial Vector Problem?

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In summary, the person in the attached photo solved the problem in a different way than the one described in the post. Their approach involved working in the opposite direction of the compass directions.
  • #1
guyvsdcsniper
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Homework Statement
Graphically determine the resultant of the following three vector displacements: (1) 24 M, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south.
Relevant Equations
Vy=Vsintheta
Vx=VCostheta
I got the attached photo from someone who solves physics problems on youtube. As you can see their final answer is 6.7i+16j. I understand how she got these values but I came out with something slightly different. I solved for the x and y components on the opposite side of each vector. So basically I came out with 16i+6.7j. Both answers make sense but I believe it comes down to a matter of perspective.

I searched around on the internet and I see that many people took different approaches to this problem resulting in people either getting my answer or the attached answer.

Are they both technically right? It feels as though that a lot of these physics problems come down to a matter of perspective.
 

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  • #2
quittingthecult said:
Homework Statement:: Graphically determine the resultant of the following three vector displacements: (1) 24 M, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south.
Relevant Equations:: Vy=Vsintheta
Vx=VCostheta

I got the attached photo from someone who solves physics problems on youtube. As you can see their final answer is 6.7i+16j. I understand how she got these values but I came out with something slightly different. I solved for the x and y components on the opposite side of each vector. So basically I came out with 16i+6.7j. Both answers make sense but I believe it comes down to a matter of perspective.

I searched around on the internet and I see that many people took different approaches to this problem resulting in people either getting my answer or the attached answer.

Are they both technically right? It feels as though that a lot of these physics problems come down to a matter of perspective.
It depends on how you are relating ##\hat i## and ##\hat j## to compass directions.
The usual would be i for E and j for N.
On that basis, what do you think the i component of "24 m, 36 degrees north of east" is? There is only one correct answer.
It might help if you compare with zero degrees N of E. Does sin or cos give the right answer?
 
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  • #3
haruspex said:
It depends on how you are relating ##\hat i## and ##\hat j## to compass directions.
The usual would be i for E and j for N.
On that basis, what do you think the i component of "24 m, 36 degrees north of east" is? There is only one correct answer.
It might help if you compare with zero degrees N of E. Does sin or cos give the right answer?
The i component should be the adjacent side of that angle which would come out to be 24*cos(36). Is that correct? I've attached my work as reference (my apologies for it being a bit messy).

So would that mean the original attached image is wrong?
 

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  • #4
quittingthecult said:
24*cos(36)
Yes.
The working in the image in post #1 is wrong.
 
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  • #5
haruspex said:
Yes.
The working in the image in post #1 is wrong.
Thank you!
 

Related to Is There More Than One Way to Solve a Trivial Vector Problem?

1. What is a trivial vector problem?

A trivial vector problem is a mathematical problem that involves manipulating vectors, which are mathematical quantities that have both magnitude and direction. These problems typically involve basic operations such as addition, subtraction, and scalar multiplication.

2. Can a trivial vector problem have more than one solution?

Yes, a trivial vector problem can have multiple solutions. This is because there are often several ways to manipulate vectors to arrive at the same result. However, some problems may only have one unique solution.

3. Are there different methods for solving a trivial vector problem?

Yes, there are multiple methods for solving a trivial vector problem. Some common methods include using graphical representations, using vector components, and using trigonometric functions.

4. How do I know which method to use for solving a trivial vector problem?

The method you use for solving a trivial vector problem will depend on the given problem and your personal preference. It may be helpful to try different methods and see which one works best for you.

5. Are there any tips for solving trivial vector problems?

One tip for solving trivial vector problems is to draw a diagram to visualize the vectors and their directions. This can help you better understand the problem and determine which operations to use. Additionally, it is important to pay attention to units and make sure they are consistent throughout the problem.

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