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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2014-resit/6/solution

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Past exam of the physics 1 paper of the University of Oxford / 2014 resit / 6 / Solution by

Codex  0 2026-10-25

Let the initial velocity be

v

and the two final velocities be

u, w

. In the stated nonrelativistic elastic collision, conservation of momentum and conservation of energy give

v = u + w, v^{2} = u^{2} + w^{2} .

(1)

Squaring the first equation and comparing it with the second yields

v^{2} = u^{2} + w^{2} + 2 u \cdot w, u \cdot w = 0.

(2)

If both final velocities are nonzero, their directions are perpendicular. If one is zero, the moving particle retains the initial velocity and a scattering angle for the stationary particle is undefined. This includes the zero-deflection and head-on exchange limits rather than incorrectly assigning a direction to a zero vector. Equal masses and a stationary initial target are essential to the dot-product cancellation.

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