Kinematics question -- Adding and subtracting vectors

This can be found using the Pythagorean theorem. The magnitude of a vector (a,b) is just the square root of the sum of the squares of the coordinates, or √(a²+b²). So, in this case, the magnitude of vector a is √(1.25²+6.125²) = √(7.765625) = 2.79, and the magnitude of vector b is √(5.75²+(-3.125)²) = √(33.015625) = 5.74. In summary, the magnitude of vector a is 2.79 and the magnitude of vector b is 5.74.
  • #1
chardy87

Homework Statement


If vector
a
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is added to vector
b
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,
the result is the vector
c
rightarrowhead.gif
= (7.00, 3.00).
If
b
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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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  • #2
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?
 
  • #3
The answer is supposed to be one number (2.00 for example). I'm unsure how to get this as I have coordinates.
 
  • #4
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.
 
  • #5
No I do not know how to do that.
 
  • #6
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:
  • #7
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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Related to Kinematics question -- Adding and subtracting vectors

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It involves the use of mathematical equations and graphs to describe the position, velocity, and acceleration of an object over time.

2. How do you add vectors in kinematics?

In kinematics, vectors can be added using the vector addition or parallelogram method. This involves placing the vectors tip-to-tail, drawing a parallelogram, and finding the resultant vector from the diagonal of the parallelogram.

3. Can you subtract vectors in kinematics?

Yes, vectors can be subtracted in kinematics using the same methods as adding vectors. However, when subtracting, the direction of the vector being subtracted must be reversed before adding it to the other vector.

4. How do you find the magnitude of a vector in kinematics?

The magnitude of a vector in kinematics can be found using the Pythagorean theorem. This involves squaring the x-component and y-component of the vector, adding them together, and taking the square root of the sum.

5. What is the difference between scalar and vector quantities in kinematics?

Scalar quantities only have magnitude and no direction, while vector quantities have both magnitude and direction. In kinematics, examples of scalar quantities include distance and speed, while examples of vector quantities include displacement and velocity.

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