# Can someone explain?

1. Feb 8, 2004

### Rebel_Yell

How do you set up equations for sum of forces in the x and y directions? I can do the y when it is only moving in the x direction, but I don't know how to set up the x equation.

2. Feb 8, 2004

### HallsofIvy

Staff Emeritus
Yes, of course, you can do the "y direction when it is only moving in the x direction" because that's trivial! I'm not sure what you really meant.

Normally one starts with "movement in a line" where we only have to worry about one direction. If something is moving on the x-axis with a force in the x-direction then vx= at+ v0 and x= (1/2)at2+ v0t+ x0.

Now you have motion in the plane (or 3 dimensions with x, y, z) so you have to separate everything into x, y, z components. If you are given "initial velocity" or "force vector" as length and direction, then you need to use trigonometry to decompose into x and y components. For example if the problem says "the initial speed is 20m/s at a direction 30 degrees above the x-axis, draw a picture showing a line at 30 degrees above the x-axis. Mark off a "length" of 20 on that line and draw a perependicular from that point to the x-axis. You see a right triangle with hypotenuse of length 20, "near side" along the x-axis (so its length is x), and "opposite side" parallel to the y-axis (so its length is y). Remembering that "sine" is defined as "opposite over hypotenus", sin(30)= y/20 or y= 20sin(30). Remembering that "cosine" is defined as "near side over hypotenuse", cos(30)= x/20 or x= 30 sin (30).
Once you have those components, you can just work with "x" and "y" separately- that's the nice thing about using components.