# Homework Help: Kinematics in 2 Dimensions: Vector addition

1. Sep 22, 2010

### huybinhs

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

With the diagram and the data answer the question: What is the magnitude of A + B?

http://i995.photobucket.com/albums/af79/huybinhs/w.gif

DATA: theta1 = 33.7 deg, theta2 = 141.9 deg , A = 3.6cm, B =8.3cm.

2. Relevant equations

This is an example of vector addition. You have to add the x and y components independently and then use the theorem of Pythagoras. The figure is not to scale.

3. The attempt at a solution

I did as follow:

Ax = 3.6 * cos(33.7) = 2.995 m

Ay = 3.6 * sin(33.7) = 1.997 m

Bx = - 8.3 * sin (141.9) = -5.121 m

By = 8.3 * cos 141.9 = -6.532 m

A+B = sqrt[ (2.995 -5.121)^2 + (1.997 - 6.532)^2 ] = 5.001 = answer, but it's showing wrong!!!

Could u tell me what's wrong? Thanks!

2. Sep 22, 2010

### Thaakisfox

Thats not good what i wrote. your mistake is with the By that shouldnt be negative. as it is positive

3. Sep 22, 2010

### huybinhs

If so, 9.297 = answer => still INCORRECT :( ???

4. Sep 22, 2010

### Thaakisfox

You messed it up with sine and cosine of the 141.9 angle. Calculate the components of the B vector again.

5. Sep 22, 2010

### huybinhs

so, I agree By will be positive, but By = 8.3 * cos(141.9) which is negative number!!! I'm confused!!!

6. Sep 22, 2010

### Thaakisfox

Yes. take a look at the diagram. if you take cos(141.9) what you get is not By. since 141.9 is an angle greater than 90 degrees so actually you will get the negative of Bx.
To get the correct answer take By=8.3cos(141.9-90) and Bx=-8.3*sin(141.9-90).

7. Sep 22, 2010

### huybinhs

Thanks! Got it finally! ;)