A particle of mass m1 makes a perfectly elastic collision with a stationary particle of mass m2, where m1 > m2. What is the largest possible angle by which the incoming particle can be deflected after the collision?

arcsin(m2/m1)
arcsin(m1/m2)
arccos(m2/m1)
arctan(m2/m1)

Correct answer: arcsin(m2/m1)

Solution

For m1 > m2 the heavy particle cannot be scattered backward; the maximum lab-frame deflection angle satisfies sin(theta_max) = m2/m1.

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