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.

Jack travels in a quarter circle path.

While Jack is falling, the ladder should look something like this at all times.

A-----D
|\   /|
| \ / |
|  J  |
| / \ |
|/   \|
B-----C

AB is the wall, BC is the ground, AC is the ladder, and J is Jack.  Make a new point D so that ABCD is a rectangle.  Since diagonals of a rectangle are always even, and always  bisect each other, BD=AC and they intersect at J.  So the path that Jack follows is the same path he would follow if the ladder fell backwards instead of sliding backwards.  This path is a quarter circle with a radius half the length of the circle.

Posted by Tristan on 2004-07-27 14:41:58