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 $\theta$ to its initial direction and has a speed $v/3$. The second block's speed after the collision is:
(2015 Re)
Solution:
In an elastic collision between two equal masses where one is initially at rest, the angle between final velocities is $90^\circ$, yielding $v^2 = v_1^2 + v_2^2$. Substituting $v_1 = v/3$, we get $v_2 = \sqrt{v^2 - (v/3)^2} = \frac{2\sqrt{2}}{3}v$.
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