Question

Prove that in the elastic collision of two objects of identical mass, with one being a target initially at rest, the angle between their final velocity vectors is always 90.

Answer 1

Before elastic collison velocites occupy the endpoints of a diameter A and B. After the collison they occypy endopints of another diameter A' and B'.

And as viewed from motionless frame of reference B, the angle A'BB' is right angle, because A'B' is a diameter.

Answer 2

Χ'Χ: Ptotal(x)=P'total(x)
Y'Y:Ptotal(y)=P'total(y)
K1+K2=K1'+K2'
and we need to sow that θ+φ=90