# Combining Vectors

1. Sep 26, 2011

### MattVonFat

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.

1. The problem statement, all variables and given/known data

The question I have is:

Calculate the resultant of the two vectors shown:

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

3. 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 in to 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 (Text):

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?

Matthew

Last edited by a moderator: May 5, 2017
2. Sep 26, 2011

### Ignea_unda

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.

3. Sep 27, 2011

### zgozvrm

Your work is correct; the book has the wrong answer (I hate it when that happens)