What is the equation for combining two vectors using the parallelogram rule?

[mireazma]

I tried at "Intro physics" and was warn that my post might be deleted if not stuck to a certain template. So, here I am.
I'm an outsider in physics, yet I'm trying to make a 2d game with collisions.
I know that I can "split" a vector into two and combine two into one by this rule; I need the equation(s) for it; I remember it's complicated… Please, if know, help me

 

[Gib Z]

I think you may be talking about splitting a vector into its vertical and horizontal components. We know that adding vertical and horizontal vectors can make a vector pointing some other way, and we can reverse that process.

To split it basically draw a right angled triangle with the vector you want to split as the hypotenuse. labeling that V, and one of the other angles theta, we can see with simple trig the values of the other sides.

 

[mireazma]

Thank you; it's hard to apply this in what I'm making, though; I basically want to know the value of a 2nd vector (v2) please take a look at my scheme, cause I got the feeling v1 not equals v2 (v2<v1).
So, how can I determine how much of the tank force is applied to the truck?
If v2 is a component of v1, as a result of splitting v1 by 2 directions, what would the other component be? I'm pretty confused

Thank you in advance.

edit:
I thought v2 was the acting component of v1 upon truck; where was I thinking?!

 

[mireazma]

The very formula of parallelogram vectors merge?

Ok, forget anything else!
Anywayz, I have 2 vectors; I know the directions and the values for both; what's the formula for finding the resulting merged vector direction and value? (the vectors aren't perpendicular)
I need an equation, something, cause the computer can't see a parallelogram; he sees things a little different :)

 

[mireazma]

almost there

I found the formula for the value:

R=sqrt(V1²+V2²+2*V1*V2*cos(α))

As for the direction, I'm stuck at:

sin(β)=V2*sin(α)/R

I need β; how can I pull out β in this equation?

 

[Gib Z]

You need to use the arc sine function, which is the inverse of the sine function, just like the square is the inverse of square rooting, they reverse each others processes. You may want to look up arc sine in google.

 

[mireazma]

Thanks a lot! After asiduous searching on the web, I realized that the soft I use to make the game has arcsin already implemented. Doh!
If you sometime feel like doing simple games, go try Game Maker; it's friendly. :)