Question

Show that two balls of equal mass move
perpendicular to each other after a
two-dimensional elastic collision.

Answer 1

From the conservation of momentum:
p_i=p_f
mv_1i=mv_1f+mv_2f
v_1i=v_1f+v_2f
Then,
v_1i∙v_1i=(v_1f+v_2f )∙(v_1f+v_2f )
v_1i^2=v_1f^2+v_2f^2+2v_1f∙v_2f
From the conservation of energy:
v_1i^2=v_1f^2+v_2f^2
Thus,
v_1f∙v_2f=0
Two balls of equal mass move perpendicular to each other after a two-dimensional elastic collision.