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.
(In reply to Solution
I agree with the arc (or 1/4 circle idea).
I don't understand how you get the ladder being the tangent to the arc.
put the wall on the left, and the base of the ladder sliding to the right. Initially (theoretically), the ladder is strait up, and his motion is strait to the right, which make the ladder perpindicular to his motion. When the hieght on the wall matches the base away from the wall, yes at that point in time the ladder would be the tangent to the arc. Then at the bottom of his trip, the ladder and motion are perpindicular again.
Follow-up....what would be the formula to calculate the difference between the real angle of the ladder and the tangent at that point in time???? Better yet, how would describe in English the concept. Maybe this would be a good post in Algorythms!
Posted by Jim
on 2004-07-27 14:21:20