Adding Vectors with Given Lengths and Angle: A Basic Vector Problem

[OrigamiCaptain]

Homework Statement

I included the problem as an attachment. There is not question other than the problem. It was on a white board.

Homework Equations

I have no idea what to do with the downwards vector. I vaguely remember that I can't do anything, but I'm not sure.

The Attempt at a Solution

In the second attachment.

Thank you everyone for your help. I really want to understand this.

PS. My notation is a total disaster. What is the Y and what is the X?

 

[sun18]

Are you adding the two vectors together? Is that the problem?

I'm going to assume so. In terms of notation, it is best just to choose an x-y coordinate system to place your vectors. Also, try drawing them both originating from the same point. After you set up a coordinate system, decompose each vector into it's x and y components (using trig) and see where to go from there.

 

[OrigamiCaptain]

Are you adding the two vectors together? Is that the problem?

I'm going to assume so. In terms of notation, it is best just to choose an x-y coordinate system to place your vectors. Also, try drawing them both originating from the same point. After you set up a coordinate system, decompose each vector into it's x and y components (using trig) and see where to go from there.

I'm still really confused. I feel like I'm close, just not quite there...

 

[OrigamiCaptain]

Ok so I went to sleep and tried looking at it again in the morning. I figured out were my x and y should go so that is no longer an issue. I used 65% for my angle and got 12.68 for my x just like before and 18.9 for my y. Again not sure if this is right, but I'll definitely understand how to do this once I figure it out.

If anyone else has any ideas that would be really helpful. Thanks.

 

[Fredrik]

I'm not sure exactly what you did, but some of the numbers you got match my results, so you're probably on the right track, if you haven't solved the problem completely.

If I understand you correctly, then you're supposed to add two vectors with lengths 10 and 14, and the only additional information you have is that the angle between them is 25°. I would denote the one of length 14 by u, and the one of length 10 by v, and I would choose the coordinate system so that u is on the x axis. Then do you see what the x and y coordinates of u and v are? Once you have u and v in the form $(u_1,u_2)$ and $(v_1,v_2)$, you can just use the definition of addition: $u+v=(u_1,u_2)+(v_1,v_2)=(u_1+v_1,u_2+v_2)$. Since no coordinates were given in the problem statement, you may want to also find $|u+v|$ and the angle that $u+v$ makes with the x axis.