Find the x and y components of the following displacement.

In summary, the angle is 52 degrees west of north, resulting in a triangle with angle A being 38 degrees and angle B being 52 degrees. Using trigonometric functions, we can calculate the components of the triangle, with the x component being 15.8m west and the y component being 12.3m north.
  • #1
1irishman
243
0

Homework Statement


20m 52deg W of N


Homework Equations


trig functions



The Attempt at a Solution


I got 20cos52=12.3m west
and 20sin52=15.8m north

yet the answer in the book says 12.3m north and 15.8m west. I don't understand...I thought cos was the x component and sin was the y component. so 15.8 m north is y and 12.3m west is x no? Please help me understand how the triangle and its components would look so i may recreate on paper?
Thank you.
 
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  • #2
The angle is 52 degrees west of north. So you start at north and rotate 52 degrees to the left. The triangle will look similar to this:

Code:
Angle B -> |\
           | \
           |__\ <- Angle A

Angle A is 38* and Angle B is 52*.

Hope this helps.
 
  • #3
I thought angle A would be 52*
 
  • #4
Take a look at this:

2gvr2wg.jpg


The angle 52* West of North results in line c (note that in my pretty drawing, angle C and side c have no relation). Angle C is 52*, and since the axis are perpindicular, angle A + angle C needs to equal 90*, so A is equal to 38*.

So then cos(A) = b / c -> b = c * cos(A)
and, sin(A) = a / c -> a = c * cos(A)
 
  • #5
I figured it out a different way, but thank you for the help anyway.
I got Ry/20=cos52* so Ry=20cos52*=12.3m north
I got Rx/20=sin52* so Rx=20sin52* =15.8m west
 
  • #6
how do i get graphics like that to draw triangles etc?
 
  • #7
I just used paint.
 

1. What are x and y components in a displacement?

The x and y components in a displacement refer to the horizontal and vertical distances traveled, respectively. They represent the change in position in the x and y directions.

2. How do you find the x and y components of a displacement vector?

To find the x and y components of a displacement vector, you can use the Pythagorean theorem and trigonometric functions. The x component is given by the magnitude of the displacement multiplied by the cosine of the angle it makes with the x-axis. The y component is given by the magnitude of the displacement multiplied by the sine of the angle it makes with the y-axis.

3. What is the difference between a scalar and vector displacement?

A scalar displacement only has a magnitude, while a vector displacement has both magnitude and direction. Scalar displacements are described by a single value, while vector displacements are described by multiple components, such as x and y.

4. Can the x and y components of a displacement be negative?

Yes, the x and y components of a displacement can be negative. This indicates that the displacement is in the opposite direction of the positive axes. For example, a displacement with an x component of -5 and a y component of -3 would mean the object has moved 5 units to the left and 3 units downwards.

5. How are x and y components of a displacement related to each other?

The x and y components of a displacement are related through the Pythagorean theorem. The magnitude of the displacement is equal to the square root of the sum of the squares of the x and y components. This relationship allows us to find the total displacement, as well as the direction of the displacement using trigonometric functions.

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