Combining like terms in a physics problem

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Homework Help Overview

This discussion revolves around a first-year university physics problem in the Mechanics subject area, specifically focusing on vector operations and combining like terms. The original poster attempts to express a resultant vector C in terms of unit vectors and is seeking clarification on how to combine the components correctly.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster describes their attempts to combine vector components and expresses confusion about the correct method for combining like terms, particularly regarding the j-hat components. Some participants question the completeness of the information provided, noting the absence of given quantities necessary for verification.

Discussion Status

Participants are actively engaging in clarifying the problem setup and addressing the original poster's confusion about combining vector components. Guidance has been offered regarding the addition of i-hat and j-hat components separately, but there is no explicit consensus on the overall approach to the problem.

Contextual Notes

There is a mention of a picture that accompanies the problem, which may provide additional context, but it has not been shared in the discussion. The original poster's understanding of the problem setup appears to be incomplete, as noted by other participants.

dark-ryder341
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This is for a first year university question in Physics (Mechanics).


1. Write each vector in terms of the unit vectors i(hat) and j(hat). Use the unit vectors to express the vector C\rightarrow where C\rightarrow = 3.00A\rightarrow - 4.00B\rightarrow. Find the magnitude and direction of C\rightarrow.



Homework Equations



A\rightarrow = Axi(hat) + Ayj(hat)
Ax = 3.60cos(70deg.)=1.23
Ay = 3.60sin(70deg.)=3.38
A\rightarrow = 1.23i(hat) + 3.38j(hat)

B\rightarrow = Bxi(hat) + Byj(hat)
Bx = -2.4cos(30deg.)=-2.078
By = -2.4sin(30deg.)=-1.2
B\rightarrow = -2.078i(hat) + (-1.2)j(hat)


The Attempt at a Solution



C\rightarrow = 3.00A\rightarrow - 4.00B\rightarrow
C\rightarrow = 3.00(1.23i(hat) + 3.38j(hat)) - 4.00(-2.0781i(hat) + (-1.2)j(hat))
C\rightarrow = (3.69i(hat) + 10.14j(hat)) - (-8.312i(hat) + (-4.8)j(hat))


I got stuck at this stage; I'm pretty sure up until now I've been doing it right, but now I'm a little confused about combining the like terms (ie. ihat with ihat and jhat with jhat terms). Would I, for instance with the jhat terms, go 10.14-(-4.8) which would give me a large positive number? or would I just go 10.14(-4.8) which equals 5.34, and then subtract it later (ie. -4.622i(hat) - 5.34j(hat))?

Basically, I just need to know what to do from here. I'm pretty sure I know how to solve for the magnitude and direction once I figure out these terms. Thanks very much for any help!
 
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Hi dark-ryder341, welcome to PF.

We can't help you and check your work unless you state the problem. You have only stated the question but you did not provide the given quantities. "Write each vector" implies that there are given vectors which you have but we don't. Is there a picture that goes with this?
 
Yes, sorry, there is a picture that goes with this:

29g02lx.jpg
That's it right there.

Thanks for any help :)
 
The i-hats and j-hats add just like apples and oranges. You add all the i-hats together and then separately you add all the j-hats together. That's why we use the "hats", to keep the components separate. So your first idea is correct. The j-hat component of C is 10.14-(-4.8).
 

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