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A Rumrunner (RR) and Frigate Police (FP) are separated be 5 miles.

The initial location of RR is ($x=0, y=0$). The initial location of FP is ($x=5, y=0$).

The initial locations of both the RR and FP are known by both parties.

If RR has a maximum speed of $17$ mph and FP has a maximum speed of $25$ mph,
construct a solution in minimal time for FP to ensure that at some point he will arrive at the same position as RR.

FP can assume that RR will leave his initial spot at full speed in a straight line.

Heptapod
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Bruce Berentsen
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2 Answers2

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Have FP move directly towards RR at each point in time. Since the FP's speed is greater than RR's, it will eventually catch RR regardless of RR's path.

Fimpellizzeri
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  • as he is looking for minimal time, the following proceeds: http://math.stackexchange.com/questions/244333/cat-dog-problem-using-integration – cgiovanardi Mar 20 '17 at 23:32
  • @cgiovanardi Yeah, that constraint was added to the question after I had submitted my answer. :( – Fimpellizzeri Mar 21 '17 at 03:30
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Case 1: RR proceeds in a straight line from (0,0) in the direction of (5,0)

The FP proceeds in a straight line from (5.0) in the direction of (0,0).

The FP arrives at the position of RR in 5.0 / (25 + 17) = 0.119 hours

Case 2: RR does not proceed in a straight line from (0,0) in the direction of (5,0).

The FP proceeds in a straight line from (5,0) to (0,0) in T1 = 5.0 / 25 = 0.2 hours

T2 = (0.2 * 17) / (25 - 17) = 0.425 hours

The FP arrives at the position of RR in T1 + T2 = 0.2 + 0.425 = 0.625 hours

Bruce Berentsen
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