Question:

There’s a swan in center of a circular lake who can’t take flight from the water, only on land. On the parameter of the lake there is a hunting dog that desperately wants the swan but cannot swim. So the swan must make it to the land before taking off and must do so before the dog makes it to him. The dog is almost 4 times faster than the swan and always runs to the point around the lake closest to the swan.
How can the swan get out of the lake and take flight before the dog gets him?

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C

A

P

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A

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N

I

N

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E

R

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W

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Solution: The swan would move in a spiral( always opposite the dog with respect to the center) having its angular velocity(rad/sec)= angular velocity of the dog and with a radial velocity such that their total is= max velocity of the dog. Note that this is possible only till radius=r/4. Also, note the swan is opposite to the dog w.r.t the center. Now the swan will move to the farthest point from the dog=3r/4. And the dog has to move distance=pi*r, which is achievable.