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Asked: 2026-05-31T16:06:22+00:00

Im not good at math, I could find everything so far, but not this

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Im not good at math, I could find everything so far, but not this one.
And I just cant figure it out. I think Im just not seeing it.
Im calculating directions, two circles collide, one has an incoming direction,
and needs to get an outgoing direction.

So far I know how to get the collision point and I can calculate the incoming/outgoing angle alfa. (Calculating the angle between two lines without having to calculate the slope? (Java))

Im stuck on constructing the outgoing line and retrieving the m or a ( y = ax + b ).

enter image description here

So, from the picture, I know y, i, alfa and the point where all lines intersect (not marked, sorry).

Could anyone help me out? Im programming in Java.

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1 Answer

  1. Editorial Team

    If momentum is conserved during a collision with a horizontal boundary, the collision will just flip the sign of m. That is the m value afterward is -1 times the m value before.

    Suppose the equation of the original line is y=mx+c and the equation of the line after the collision is y=-mx+b. At the intersection point, the x and y values are the same.

    To avoid confusion later, we’ll call the x and y-values of the collision point (X,Y) not (x,y)

    At the intersection the line equations for both lines hold (for x=X, y=Y). So, 

    Y = mX+c = -mX+b.
=> mX+c+mX = b (adding mX to both sides)
=> 2mX+c = b (collecting the terms in m)

    So the intercept of the second line (which you referred to as “m or a” in your question) is 2mX+c, where X is the x-position at which the collision occurs. Hence the equation of the second line is:

    y = -mx + (2mX + c)
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