A simple version due to Feynman of Fermats principle is analyzed. It deals with the path a lifeguard on a beach must follow to reach a drowning swimmer. The solution for the exact point, P(×, 0), at the beach-sea boundary, corresponding to the fastest path to the swimmer, is worked out in detail and the analogy with light traveling at the air-water boundary is described. The results agree with the known conclusion that the shortest path does not coincide with the fastest one. The relevance of the subject for a basic physics course, at an advanced high school level, is pointed out.

Analytic solution of the lifeguard problem

De Luca, R.
Membro del Collaboration Group
;
Di Mauro, M.
Membro del Collaboration Group
;
Naddeo, A.
Membro del Collaboration Group
2017

Abstract

A simple version due to Feynman of Fermats principle is analyzed. It deals with the path a lifeguard on a beach must follow to reach a drowning swimmer. The solution for the exact point, P(×, 0), at the beach-sea boundary, corresponding to the fastest path to the swimmer, is worked out in detail and the analogy with light traveling at the air-water boundary is described. The results agree with the known conclusion that the shortest path does not coincide with the fastest one. The relevance of the subject for a basic physics course, at an advanced high school level, is pointed out.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4705127
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