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 re: Solution
Now we know Jack's travel is a 1/4 circle.
The angle formed where the wall meets the gound is 90 degrees.
As Jack tavels, the angle @ decreases from 90 to 0. There is a point where he is equal distance from the ground and the wall, and this angle is 45 degrees. This is the point where the tangent line to the arc is super imposed on top of the ladder. Both having a slope of -1.
Before this point, the difference between the slopes of the ladder and the tangent line are decreasing from 90 degress to zero, then increase back up to 90 degrees.
If you take the angle where Jack is at, double it, the subtract it from 90, take the absolute value, THEN you get the angle difference between the slopes.....
Posted by Jim
on 2004-08-10 10:06:19