8. Sliding Stick I
Setup
A stick of length 1 stands upright against a wall.
The bottom slides outward; the top slides down.
Rules
- The stick maintains contact with both wall and ground
- Motion ends when the stick lies flat
Question
How far does the midpoint travel?
Answer format
Enter a number rounded to 2 decimal places.
Your Answer
Need help?
Hint 1
Parameterize the position of the stick using the angle it makes with the ground, or the horizontal distance of the bottom.
Hint 2
If the bottom is at (t, 0) and top at (0, sqrt(1-t²)), where is the midpoint?
Hint 3
What shape does the midpoint trace as the stick slides?