The Sandpiper

Calculus Level 5

While walking on a straight path on the flat wet sand on the beach, you approach a sandpiper directly ahead of you in the line of your path. The sandpiper does not move until you are at distance \(X\) from it. Then it starts moving away from you at a constant speed in an arc, maintaining the same distance \(X\) from you, so that when you are at where the sandpiper was originally, the sandpiper is now at distance \(X\) from you perpendicularly to the line of your path. As you continue on, the sandpiper continues on the same arc around behind you, so that it eventually comes back to exactly where it was before you interrupted his feeding, and hopes you won't bother it again.

If you were walking at 1 meter per second, how fast did the sandpiper walk?

Note: The arc is not any part of a circle. Also, speed is tangential speed on arc.

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