Conservation of momentum assuming equal masses Steps:

• Define right as positive direction: initial velocity of X is -5 m/s (left), Y is +15 m/s (right).
• Total initial momentum: m(-5) + m(15) = 10m (rightward).
• After collision, Y has velocity +7 m/s, so m v_X + m(7) = 10m.
• Simplify: v_X + 7 = 10, so v_X = 3 m/s (to the right).

Why B is correct:

• It matches the result from momentum conservation, where equal masses imply the center of mass velocity is preserved at ( -5 + 15 ) / 2 = 5 m/s; post-collision, (3 + 7)/2 = 5 m/s.

Why the others are wrong:

• A: Assumes X reverses but underestimates speed; ignores net rightward momentum.
• C: From elastic relative velocity reversal (v_X - 7 = -20), but requires unequal masses.
• D: Half of elastic case with switched directions; doesn't conserve momentum.

Final answer: B