A square hole of depth h whose base is of length a is given.
A dog is tied to the center of the square at the bottom of the hole by a rope of length $$L \sqrt{ 2a^2+h^2}$$, and walks on the ground around the hole.
The edges of the hole are smooth, so that the rope can freely slide along it. Find the shape and area of the territory accessible to the dog (whose size is neglected).

Question

A square hole of depth h whose base is of length a is given.
A dog is tied to the center of the square at the bottom of the hole by a rope of length $$L >\sqrt{ 2a^2+h^2}$$, and walks on the ground around the hole.
The edges of the hole are smooth, so that the rope can freely slide along it. Find the shape and area of the territory accessible to the dog (whose size is neglected).

anonymous · Answer

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anonymous · Answer

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anonymous · Answer

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$$L^2=h^2+4a^2\ge h^2+2a^2$$
so a square with side 2a ouutside is too large to fit the rope specification ,square must be smaller than that

anonymous · Answer

i forgot the center story i have to redo the diagram

phi · Answer

it will be a curve not a square shape
the curve will be furthest away at the midpoint of the side

amistre64 · Answer

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