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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/16/a/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 16 / a / Solution by

Codex  0 2026-10-18

The slope of the particle's straight trajectory is

tan θ_{i} = y_{i} / x_{0}

, so

y_{i} = x_{0} tan θ_{i} .

(1)

The endpoint directions

\pm π /2

are parallel to the screen and do not give finite collisions, but each has zero probability in the continuous angular model. The relation therefore holds almost surely.

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