Pyhsics addition of vectors....help?

The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 11.0 m, C = 12.0 m, and D = 31.0 m. Determine the magnitude and directional angle for the resultant that occurs when these vectors are added together.





for the picture go to:





http://img299.imageshack.us/img299/9572/...





thanks

Pyhsics addition of vectors....help?
First measure all the angles from the positive X axis going in a counterclockwise direction





A = 15m%26lt;160 deg


B = 11m%26lt;90 deg


C = 12m%26lt;215 deg


D = 31m%26lt;310 deg





Then convert each vector into X and Y components using the following formula





V = cos(a)*|v|*X + sin(a)*|v|*Y





so





A = cos(160)*15*X + sin(160)*15*Y


B = cos(90)*11*X + sin(90)*11*Y


C = cos(215)*12*X + sin(215)*12*Y


D = cos(310)*31*X + sin(310)*31*Y





Then simply sum each parts





let say that





R = Rx*X + Ry*Y





Rx = cos(160)*15+cos(90)*11+ cos(215)*12+cos(310)*31


Rx = -4.00





Ry = sin(160)*15+sin(90)*11+ sin(215)*12+sin(310)*31


Ry = -14.50





So





|R| = sqrt(Rx^2 + Ry^2) = 15.04


R%26lt; = invsin(-14.5/15.04)= -74.6 degree





Now adjust the angle by looking at the rectangular coordinate. The result is right but you have to use the mirror image of the angle with respect to the Y axis (180+74.6). You have to look at the rectangular coordinate (-4,-14.5) to understand this and note that


sin(-74.6) = sin(180+74.6)





|R| = sqrt(Rx^2 + Ry^2) = 15.04


R%26lt; = invsin(-14.5/15.04)= 254.6 degree
Reply:First using trigonometry you need to break each vector into its component forces in the x and y directions. Example for A:





Using the 15*sin(30)=5.1 and 15*cos(30)=14.1, your components are x = -14.1 (since it points right to left) and y = 5.1.





Doing this for each and then adding each of the x and y components, I came up with:





B: x = 0; y = 11


C: x = -12.3; y = -6.9


D: x = 19.9; y = -23.7





For a sum total of x = -6.5 and y = -14.5.





Now you can use tan^-1(6.5/14.5) to find the angle equal to 65 degrees from the x-axis in the third quadrent.





And the magnitude is sqrt(6.5^2 + 14.5^2) = 15.9