Combining Vectors: Calculate Resultant | Matthew vonFat

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In summary, a learner is seeking help with a question from a home learning course. They have calculated the magnitude and direction of the resultant of two vectors, but their answer does not match that given in the course book. They share their calculations and ask for confirmation of their work. Other members confirm that their calculations are correct and point out that the book has the wrong answer.
  • #1
MattVonFat
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It's not exactly homework as it's a progress check question in a home learning course but I think this is the best place for it.

Homework Statement



The question I have is:

Calculate the resultant of the two vectors shown:

[PLAIN]http://www.mattvonfat.com/question.png


The Attempt at a Solution



Here's my problem, I've come up with the magnitude of the resultant as 116.037N and the direction 10.04° below the horizontal. The course gives the answer as 76.97N at 15.24° below the horizontal.

I've gone over the material again however it seems that the answer the course book gives is still wrong. I also tried putting the vectors into the vector addition applets and calculators on web pages but they don't give the answer the course gives me either.

Here's how I worked it:

Code: 
Horizontal Component of 60N vector = 60cos 35
                                   = 49.15N

Vertical Component of 60N Vector    = 60sin 35
                                    = 34.41N

Horizontal Component of 85N vector = 85cos 40
                                   = 65.11N

Vertical Component of 85N vector    = -85sin 40
                                    = -54.64N

Total Horizontal = 49.15 + 65.11 = 114.26N

Total Vertical = 34.41 - 54.64 = -20.23N

Then I use those values for the sides of a right angled triangle and the hypotenuse/magnitude of the vector is:

h² = 114.26² + -20.23²
h² = 13464.6
h = 116.037N

and the angle (a):

Tan a = -20.23 / 114.26
a = Tan[SUP]-1[/SUP] 0.177
a = -10.04°

Is there a problem with they way I have done it or is the course wrong?

Thanks for any help you can offer,
Matthew
 
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  • #2
Looks spot on to me.

The only place to make sure you keep an eye out is with significant figures. Depending on how closely someone wants to argue it, there are either 2 or 1 significant figure(s). But overall, very clearly and cleanly worked. :approve:
 
  • #3
Your work is correct; the book has the wrong answer (I hate it when that happens)
 

1. How do I calculate the resultant of two or more vectors?

To calculate the resultant of two or more vectors, you need to add the individual components of each vector together. This can be done by using the Pythagorean theorem for the magnitude and trigonometric functions for the direction. Once you have the magnitude and direction of the resultant, you can represent it as a single vector.

2. What is the difference between adding vectors and combining vectors?

Adding vectors involves finding the sum of the individual components of each vector. Combining vectors, on the other hand, involves finding the resultant vector by using the magnitude and direction of each vector. In essence, combining vectors is a more comprehensive way of adding vectors.

3. Can vectors be combined if they are not in the same direction?

Yes, vectors can be combined even if they are not in the same direction. This is because the direction of the resultant vector is determined by the angle between the individual vectors. If the vectors are not in the same direction, the angle between them will be taken into account when calculating the direction of the resultant.

4. How can I represent the resultant vector graphically?

The resultant vector can be represented graphically by drawing the individual vectors as arrows on a coordinate plane and then drawing the resultant vector from the tail of the first vector to the head of the last vector. The magnitude of the resultant can be represented by the length of the arrow, and the direction can be represented by the angle of the arrow.

5. Are there any special cases when combining vectors?

Yes, there are two special cases when combining vectors: when the vectors are parallel and when the vectors are perpendicular. When the vectors are parallel, the magnitude of the resultant is the sum of the individual magnitudes, and the direction is the same as the individual vectors. When the vectors are perpendicular, the magnitude of the resultant is found using the Pythagorean theorem, and the direction is 90 degrees from the individual vectors.

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