On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another

Question

On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $	heta$ to its initial direction and has a speed $v / 2$. The second block's speed after the collision is\

Professor PC Thomas Classes · Answer

(b) : By conservation of KE: $\frac{1}{2} M v^{2}=\frac{1}{2} M(v/2)^{2}+\frac{1}{2} M v^{\prime 2}$. $v^{2}=\frac{v^{2}}{4}+v^{\prime 2} \implies v^{\prime 2}=\frac{3}{4} v^{2} \implies v^{\prime} = \frac{\sqrt{3}}{2} v$.