Oblique Collisions

jsmith613

In an oblique collision (when one object hits another object of IDENTICAL mass at a slight angle the two objects move at right angles to each other.

my book says

p² = p₁² + p₂²

For momenum conservtation:

p= p₁+ p₂

apparently these equations can only be consistent of the collision occurs at right angles. why?

haruspex

These are vectors, right?
p.p = (p1+p2).(p1+p2) [2nd equn]
= p1.p1 + 2.p1.p2 + p2.p2
= p.p + 2.p1.p2 [1st equn]
Hence p1.p2 = 0

jsmith613

where has p2.p2 gone in the final line
surely the final line should be
= p1.p2 + p2.p2, no?

haruspex

1st equn says p.p = p1.p1 + p2.p2
To get from my second line to my third line, use this to substitute p.p for p1.p1 + p2.p2.