Kinematics in 2 Dimensions: Vector addition

AI Thread Summary
The discussion revolves around solving a vector addition problem involving two vectors A and B with given magnitudes and angles. The initial calculations for the components of vectors A and B were incorrect, particularly with the signs of the components due to the angles being in different quadrants. Participants clarified that the cosine and sine functions needed to be adjusted based on the angles' positions on the unit circle. After correcting the calculations, the correct components were established, leading to the accurate magnitude of the resultant vector A + B. The final consensus confirmed the importance of understanding vector direction and quadrant placement in calculations.
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Homework Statement



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.

Homework 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.

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!
 
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Thats not good what i wrote. your mistake is with the By that shouldn't be negative. as it is positive
 
Thaakisfox said:
Thats not good what i wrote. your mistake is with the By that shouldn't be negative. as it is positive

If so, 9.297 = answer => still INCORRECT :( ?
 
You messed it up with sine and cosine of the 141.9 angle. Calculate the components of the B vector again.
 
Thaakisfox said:
You messed it up with sine and cosine of the 141.9 angle. Calculate the components of the B vector again.

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

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