Calculating Displacement: X Component Error

In summary, the car traveled 2.2km in the x-direction and then turned left 67.5 degrees to the original direction and traveled an additional 3.09km in the northeast direction. The x component of the car's displacement was incorrectly calculated by the person, but they later realized they had made a mistake and corrected it.
  • #1
AdnamaLeigh
42
0
I thought I calculated the vector components correctly and added them, but apparently something is wrong.

A car travels 2.2 km in the x-direction, then turns left 67.5 degrees to the original direction and travels an additional distance of 3.09km. Calculate the x component of the car's displacement.

This is what I did:

The first vector went 2.2km to the right, so the x component of that vector is 2.2, while the y is 0. Unless I misread the info, the second vector is going 3.09km in the northwest direction. I found the x component of that by multiplying the cosine of 67.5 by -3.09 (negative because it is going in the negative x-axis direction, or so that's how my book explains it). I got -1.182. The y component is unncecessary but I got 2.855 for that. I added the two x components up and I got 1.018 and it's incorrect. I don't know where I went wrong.
 
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  • #2
If the car turns through an angle of less than 90 degrees its x-component is still positive. You should not have negated 3.09.
 
  • #3
Yeah, you're right. It's going in the NE direction. I completely messed that up, I feel like a moron. Thanks
 

1. What is the formula for calculating displacement in the X direction?

The formula for calculating displacement in the X direction is: Δx = xf - xi, where Δx is the displacement, xf is the final position, and xi is the initial position.

2. How do you calculate the X component error?

To calculate the X component error, you need to find the difference between the measured displacement and the actual displacement in the X direction. This can be expressed as: Errorx = Δxmeasured - Δxactual.

3. Can displacement in the X direction be negative?

Yes, displacement in the X direction can be negative. This indicates that the object has moved in the negative direction, or opposite to the positive direction on the X axis.

4. How do you determine the direction of displacement in the X direction?

The direction of displacement in the X direction can be determined by looking at the sign of the X component. A positive X component indicates displacement in the positive direction, while a negative X component indicates displacement in the negative direction.

5. Can the X component error be zero?

Yes, the X component error can be zero. This means that the measured displacement and the actual displacement in the X direction are the same, indicating an accurate measurement.

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