Kinematics question -- Adding and subtracting vectors

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Homework Help Overview

The discussion revolves around a kinematics problem involving the addition and subtraction of vectors. The original poster presents two vector equations that yield specific resultant vectors, and they seek to determine the magnitudes of the individual vectors involved.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the equations derived from vector addition and subtraction, with some questioning the notation used. There is also a focus on understanding how to calculate the magnitude of vectors from their components.

Discussion Status

Some participants have provided guidance on the correct notation for the equations and clarified the distinction between vector components and magnitudes. However, there is still uncertainty regarding the method to calculate the magnitudes, with multiple participants expressing confusion about the conversion from rectangular to polar coordinates.

Contextual Notes

Participants note that the problem requires the magnitudes of the vectors rather than their components, which has led to some misunderstanding. There are references to textbook resources and online searches for additional information on vector magnitudes.

chardy87

Homework Statement


If vector
a
rightarrowhead.gif

is added to vector
b
rightarrowhead.gif
,
the result is the vector
c
rightarrowhead.gif
= (7.00, 3.00).
If
b
rightarrowhead.gif

is subtracted from
a
rightarrowhead.gif
,
the result is the vector
d
rightarrowhead.gif
= (−4.50, 9.25).

what is the magnitude of a?
what is the magnitude of b?

Homework Equations

The Attempt at a Solution


a + b = (7.00, 3.00)c
a-b=(-4.50,9.25)d
2a=(c + d)
(c+d/2) = a
a=(1.25,6.13)

b =c-a
b=(5.75,-3.13)
 
Last edited by a moderator:
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chardy87 said:
(c+d/2) = a
a=(1.25,6.13)

b =c-a
b=(5.75,-3.13)
Looks mostly right, but your parenthesis is misplaced slightly in the first quoted equation above. It should be (c+d)/2 = a

But you still did the math right, it's just a typo in how you wrote the equation. Also, Does your instructor want you to round to 6.13 and -3.13, instead of 6.125 and -3.125?
 
The answer is supposed to be one number (2.00 for example). I'm unsure how to get this as I have coordinates.
 
chardy87 said:
The answer is supposed to be one number (2.00 for example). I'm unsure how to get this as I have coordinates.
Oh, I see now. They are asking for the "magnitude" of each vector, not the components of the vector. Do you know how to get the magnitude and direction of a vector in polar coordinates given the components in rectangular coordinates?

Hint -- do not round your answers until the very last step.
 
No I do not know how to do that.
 
chardy87 said:
No I do not know how to do that.
It should be in your textbook or the study materials for this problem set.

Alternately, go to Google and search on rectangular to polar conversion. :smile:
 
Last edited:
chardy87 said:
No I do not know how to do that.

You do not need to go to polar coordinates. Just Google "magnitude of vector".

Basically, a (2-dimensional) vector (a,b) is a point in the Cartesian plane, with x-coordinate 'a' and y-coordinate 'b'. The magnitude of (a,b) is just the distance from the point (a,b) to the origin (0,0).
 
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