Solutions due by high noon on Friday, Dec. 5.
Your spaceship crashes into the center of a circular pond of radius r on Mars due to a mechanical failure. When you and your crew finish repairs, you notice that there is a huge alien at the edge the pond, and it does not look friendly. Fortunately for you, it does not seem to be able to swim. Your spaceship is ready to fly but it cannot take off from the pond directly. You must reach the edge of the pond to fly away. You steer the spaceship around the pond and conclude that the alien can move four times as fast as your spaceship can on the water. Assume that the alien is smart to move around the edge of the pond trying to catch your spaceship. Is it possible for you to ever reach the edge of the pond and fly away to its escape from the ground? Provide a sound mathematical reasoning for your answer.
This problem is brought to you by Prof. Choong-Soo Lee.
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