Solving a Vector Problem: Find Magnitude & Direction

[Dreams2Knight]

[SOLVED] Vector Problem

I hope someone can help me. I am so tired of trying to figure this out.

A man pushing a mop across a floor causes the map to undergo two displacements. The first has a magnitude of 110 cm and makes an angle of 110° with the positive x axis. The resultant displacement has a magnitude of 240 cm and is directed at an angle of 25.0° to the positive x axis. Find the magnitude and direction of the second displacement. Find the angle with respect to the positive x axis.

I started by measuring 110 degrees and drew my vector starting at the origin (origin is point A). The end of this first vector is point C. Then, starting at point A again (since this vector is the resultant vector) I measured an angle of 155 degrees (180-25=155) and drew my vector, the end of which is labeled point B. I then drew the connecting vector, vector BC.

Now, I drew a line straight down from point B to the x-axis. This point is D. I need to find the x and y components of this right triangle, triangle ABD. By using the angle of 155 degrees I can say cos155=x divided by 240. This equals -217.5139. To find y, I can say sin155=y divided by 240. This is 101.4284.

Now, I drew a line from point C straight over to the y-axis. This will be point E. I need to find the components of triangle ACE. So, cos110=x divided by 110. This is -37.6222. And sin110=y divided by 110. This is 103.3662.

This is the point where I'm not sure what to do. Since the unknown vector, BC, is a hypotenuse of a third right triangle, I just don't know what to do next. I thought I could take the difference of the x values and y values I found, then use the Pythagorean theorem to get vector BC, but I get the wrong answer. (I keep getting vector BC equals 180.)

I hope I was able to explain what I did without confusing anyone. I would be ever so grateful for some help.

 

[hage567]

I measured an angle of 155 degrees (180-25=155) and drew my vector

I don't understand what you're doing here. Why not draw it at 25 degrees? That's the direction it's supposed to point, as stated in the problem. Maybe I'm just not picturing what you did.

I haven't gone through your entire solution since I don't get what you did above, but I don't think you need to worry about finding the components of anything here. If you draw the two vectors given you can easily find the magnitude and direction of the "second displacement" by the cosine law and the sine law.

Hope that helps.

 

[Dreams2Knight]

I don't understand what you're doing here. Why not draw it at 25 degrees? That's the direction it's supposed to point, as stated in the problem. Maybe I'm just not picturing what you did.

Oh my god, I don't know why I thought the 25 degrees had to measured from the 180 degree line! My mind is so confused, I guess I just got it turned around with another problem I was doing. Some of the other problems I'm doing do give you the angle from the 180 degree line.

I"m going to rework the problem. I'll post my results.

 

[Dreams2Knight]

Urgh. I'm STILL getting the same answer. I've done all I can do tonight. I've got to sleep. I'll work on this again tomorrow.

 

[alphysicist]

Hi Dreams2Knight,

Your procedure of subtracting the x and y values to give the x and y components of BC, and then using the Pythagorean theorem, sounds like the right thing to do. What numbers did you use and get?

It's difficult to follow without knowing the numbers that you actually plugged in, but perhaps you made an error in subtracting the x values? If you did not take into account that one of the x values was negative, the mistake would lead to a final answer of about 180.

 

[Dreams2Knight]

Hi Dreams2Knight,

If you did not take into account that one of the x values was negative, the mistake would lead to a final answer of about 180.

Ah, well that was the problem. I didn't use the negative. I now have the correct answer! Something so simple caused me so much grief. Thank you for bringing that to my attention. I sure appreciate the help.