What is the method for finding the resultant of displacement vectors?

[Rawr]

Problem: Find the resultant of the three displacement vecotrs in the drawing by means of the component method. The magnitudes of the vectors are A = 5.00 m, B = 5.00 m, and C = 4.00 m.

http://img179.imageshack.us/img179/6690/picturels2.jpg <-- there's the picture.

I found the trigonometric functions of A and B. For A... 5 sin (20 degrees) = 1.71 m. 5 cos (20 degrees) = 4.70. Then for B... 5 sin (60 degrees) = 4.33. 5 cos (60 degrees) = 2.50.

Am I heading in the right direction? Or am I completely off course? If I am heading in the right direction, what do I do next? Do I subtract 1.71 m from 4.33 m because it's heading in the opposite direction?

The answer is 3.00 m, 42.8 degrees above the -x axis, but I have no clue how they got that answer.

 

[danago]

With these problems, i find it easy to treat the axes just like a cartesian plane. there's the origin (the point where the rays are coming from). With the horizontal component, if it is to the left of the origin, it is negative. With the vertical component, if it is below, it is negative.

So with that example, point A is ABOVE and to the LEFT of the origin. Therefore, we can say that the horizontal component will be negative, and the vertical component positive.

So the horizontal component would be: -5 cos 20
So the vertical component would be: 5 sin 20

So that with all the of the rays, and then add the components.

Another way to do it would be to instead look at the angles each ray makes with the axis, is to look at the total angle it makes from the positive y axis, clockwise. So ray A would make an angle of 290 degrees. The horizontal component will be the the product of the magnitude and the sine of this angle, and the vertical component will be the product of the magnitude and the cosine of the angle. So:

Horizontal: 5 sin 290
Vertical: 5 cos 290

And those two components match up with the first method i posted.

-5 cos 20=5 sin 290
5 sin 20=5 cos 290

Hope that helped.
Dan.

 

[pavadrin]

you could also head to tail them in a scale diagram, however as danago explained would be more accurate and is simple once you get your head around it