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The lion and the tamer


bonanova
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If a lion and his tamer can run at precisely the same speed without tiring, would the tamer be safe inside the lion's circular cage? Assume the lion sits on a stool at the center of the cage as the tamer enters though a door on the perimeter of the cage. You can also neglect the size of their bodies. i.e. consider the lion and tamer as points.

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Neglecting inertia and response time of the lion, The tamer would always be caught if he is required to change direction (regardless of the shape of the cage). because each time the tamer changes with even the slightest direction at the slightest angle, the lion will be able to switch to the shortest direction to where the tamer is (even if blindly following him).

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Well, yes if the tamer can control the lion.

If he cannot then he is unsafe because the lion can attack him by judging where the tamer will reach(here it is assumed that the tamer runs along the periphery and the distance travelled by the tamer till the lion catches him is more than the radius of the cage).

Edited by Chandra002
Missed a bracket
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  On 4/21/2016 at 2:40 PM, Chandra002 said:

 unsafe because the lion can attack him by judging where the tamer will reach...

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Hi and welcome Chandra.

Let's add the condition that the tamer (and the lion) can change/reverse directions instantaneously.
Tamer can switch from CW to CCW at his pleasure.

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Good thinking. Let's add the condition that the lion and tamer are point objects. Can they coincide?

Also, could the lion reduce the radius of his circle to that of the lion and maintain any angular separation he might at some point have obtained? (Your solution prohibits this, but suppose the lion made one misstep and just for a moment he lagged the angle of the tamer.) This question has an amusing answer.

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Greetings, Prof. T. Great to hear from you.

The lion does start from the center, sadly for the tamer.

The prevailing thought is for the lion to maintain the tamer's azimuth (his radius is shorter) and inch his way outward. By maintaining his azimuth, never leading nor lagging, the lion does not permit the tamer to gain advantage by reversing his direction. Although, since he can do so instantaneously, neither would the tamer lose advantage.

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