A mass m moves with a given speed and collides (not necessarily head-on) elastically with another mass m that is initially at rest, as shown in Fig. Which of the figures shows an impossible outcome for the two velocities? (The velocities are drawn to scale)

Question

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For an elastic collision of equal masses with one initially at rest, the two final velocities must be perpendicular and must add (as vectors) to the initial velocity.

(A) Both final velocities vertical: total momentum zero, not the initial horizontal momentum - impossible. (B) and (C) Collinear pairs with both nonzero: $v_{1} \pm v_{2} = v$ with $v_{1}^{2} + v_{2}^{2} = v^{2}$ forces one to be zero - impossible as drawn. (D) The angle is obtuse and the vertical components do not cancel - violates perpendicularity and momentum.

Ans. (A,B,C,D)

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