Kinematics in 2 Dimensions: Vector addition

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Homework Help Overview

The discussion revolves around a problem in kinematics, specifically focusing on vector addition in two dimensions. The original poster presents a scenario involving two vectors, A and B, with given magnitudes and angles, and seeks to determine the magnitude of their resultant vector.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of vector components, particularly questioning the signs of the components derived from the angles provided. There is an exploration of the correct application of trigonometric functions to determine the components of vector B.

Discussion Status

Some participants have offered guidance on recalculating the components of vector B, suggesting that the original calculations may have misapplied trigonometric functions. The conversation reflects a mix of attempts to clarify the correct approach and the ongoing confusion regarding the signs of the components.

Contextual Notes

There is mention of a diagram that is not to scale, which may contribute to the confusion in interpreting the angles and components. Participants are also grappling with the implications of angles greater than 90 degrees on the signs of the vector components.

huybinhs
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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! ;)