Calculating Displacement: X Component Error

AI Thread Summary
The discussion centers on calculating the x component of a car's displacement after it travels in two segments. The first segment is 2.2 km in the positive x-direction, while the second segment involves a turn of 67.5 degrees and a distance of 3.09 km. The error arose from incorrectly negating the x component of the second vector, which should remain positive since the car is moving in a northeast direction. The correct approach involves using the cosine of 67.5 degrees without applying a negative sign. The clarification highlights the importance of accurately interpreting directional changes in vector calculations.
AdnamaLeigh
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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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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.
 
Yeah, you're right. It's going in the NE direction. I completely messed that up, I feel like a moron. Thanks
 

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