Bang! - Futility Closet

Bang!

A curious puzzle from Pi Mu Epsilon Journal, Fall 1968 [Volume 4, Issue 9]:

Where must a man stand so as to hear simultaneously the report of a rifle and the impact of the bullet on the target?

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Image: Wikimedia Commons A hyperbola is the locus of points the difference of whose distances from two fixed points is a constant. In this case that constant is the distance that sound travels in the length of time it takes the bullet to reach the target. The man can stand anywhere on the branch of the hyperbola nearer to the target — “but hopefully not at the vertex.” (Proposed by Thomas Dobson of Hexham, England; solved by C.W. Dodge of the University of Maine, Orono, in Fall 1969 [Volume 5, Issue 1].)