Even though it was now middle of winter, Jack hauled out his ladder and placed his ladder against the side of the house and began to climb. He had some bad luck when he reached the half-way point. The ground was a frozen sheet of ice and the base of his ladder slipped out and the top slid down the side of the house. Jack, clinging to the center rung, wound up moving from Point A on the side of his house to Point B on the ground.

Describe the path Jack traveled.

My first guess would be hyperbolic or parabolic. Intuitively, when the ladder is vertical (against the wall), the midpoint will move more rapidly outward than downward. Around halfway, 45 degrees, it will of course be moving at about the same rate in both directions, and near the end of the fall, with the ladder horizontal above the ground, he will be falling more rapidly downward.

That's just my first thought, though, and I don't have anything to back it up...

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Posted by DJ on 2004-07-27 11:10:59