A ball collides elastically with another ball of the same mass. The collision is oblique and initially second ball was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocities of the balls after the collision?
Applying law of conservation of momentum along direction of initial velocity we get
mu=mv(cos θ1+cos θ2)
Applying law of conservation of momentum perpendicular to direction of initial velocity
0=mv sin θ1−mv sin θ2⇒θ1=θ2mu=2 mv cos θ [θ1=θ2=θ]cos θ=u2v (ii)
According to law of conservation of KE,
12mu2=12mv2+12mv2u2=2v2 or u=√2v (iii) From Eqs. (ii) and (iii), we have cos θ=√2v2v
or cos θ=1√2 or θ=45∘θ1+θ2=90∘