Question: A physics student playing pocket billiards wants to strike her cue ball such that it hits a cushion and then hits the eight ball squarely.

A physics student playing pocket billiards wants to strike her cue ball such that it hits a cushion and then hits the eight ball squarely. She chooses several points on the cushion and for each point measures the distance from it to the cue ball and to the eight ball. She aims at the point for which the sum of these distances is least.

(a) Will her cue ball hit the eight ball?

(b) How is her method related to Fermat's principle?

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