All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Jack's Ladder (Posted on 2004-07-27) Difficulty: 2 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 2.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Good explanation | Comment 9 of 22 |

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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (5)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information