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Perfectly elastic collisions (proof)

  1. Dec 16, 2004 #1
    An object collides elastically (perfectly) with another object (identical object) at rest. If it is not a head on collision how can i PROVE that the angle between them afterwards is 90 degrees? :confused: :bugeye:

    I have NO IDEA on what to do...it's been puzzling me and my friends for a little while now...

    help anyone?
  2. jcsd
  3. Dec 16, 2004 #2
    In a elastic collision momentum and KE are conserved:



    in this case the masses are the same so we can simplify:



    Consider now the first equation, look at the vectors [tex]\overrightarrow{v}_1_f[/tex] and [tex]\overrightarrow{v}_2_f[/tex], if they are added they are equal to [tex]\overrightarrow{v}_1_i[/tex], so you can picture the 3 of them as forming a triangle.

    If you picture this you can see that [tex]v^2_1_i=v^2_1_f+v^2_2_f[/tex] is the Theorem of Pythagoras. [tex]\overrightarrow{v}_1_i[/tex] is the hypotenuse so the other two sides form 90º.

    I hope the explanation is clear enough.
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