Trying to separate vector into x and y components

In summary, the problem involves finding the ##x##- and ##y##-components of a vector with a magnitude of 58m/s^2 and an angle of 40° below the positive ##x##-axis. After solving using trigonometry, the components are ##-37## and ##44## (correct to two significant figures).
  • #1
cmkluza
118
1

Homework Statement


##\overrightarrow{a} = (58m/s^2, 40°## below positive ##x## - axis)
Find the ##x##- and ##y##-components of the vector.
Express your answers using two significant figures. Enter your answers numerically separated by a comma (##a_x,a_y##).

Homework Equations


None I can think of.

The Attempt at a Solution


I've already done this all out on paper, it seems like simple enough trig, and should be:
##a_x = -58sin(40) = 58sin(320) = -37## (correct to two significant figures)
##a_y = 58cos(40) = 58cos(320) = 44## (correct to two significant figures)
Therefore, the components as a comma separated list should be "##-37,44##".

Yet this is not the answer. What am I doing wrong?

Edit: I realized after drawing it out that I switched the signs for ##x## and ##y##. I'm a fool, please disregard this thread.
 
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  • #2
Have you drawn a diagram?
 

1. How do you separate a vector into x and y components?

To separate a vector into its x and y components, you can use the trigonometric functions of sine and cosine. The magnitude of the vector multiplied by the cosine of the angle gives the x component, and multiplied by the sine of the angle gives the y component.

2. Why is it important to separate a vector into x and y components?

Separating a vector into x and y components allows us to analyze and work with the vector in a two-dimensional coordinate system. It also makes it easier to calculate the vector's magnitude and direction.

3. Can you separate a vector into more than just x and y components?

Yes, a vector can be separated into any number of components, as long as there are corresponding directions for each component. For example, a vector in three-dimensional space can be separated into x, y, and z components.

4. What if the vector is not aligned with the x and y axes?

If the vector is not aligned with the x and y axes, you can use the dot product to find the projection of the vector onto the x and y axes. This projection can then be used to calculate the x and y components of the vector.

5. Are there any shortcuts or tricks for separating a vector into x and y components?

One shortcut is to use the Pythagorean theorem to find the magnitude of the vector, and then use trigonometry to calculate the x and y components. Another trick is to use unit vectors in the x and y directions to represent the components of the vector.

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