Related Rates: Sliding Ladder Against a Wall
December 10, 2025
Problem
A ladder 10m long leans against a wall. If the bottom slides away at 2 m/s, how fast is the top sliding down when the bottom is 6m from the wall?
Explanation
A 10 m ladder leans against a wall. As the bottom slides away, the top slides down. The right triangle formed obeys x² + y² = 10². Differentiating gives 2x·dx/dt + 2y·dy/dt = 0, so dy/dt = −(x/y)·dx/dt. This visualization shows the ladder, its motion, and the instantaneous rate when the bottom is 6 m from the wall.
Interactive Visualization
Parameters
10.00
2.00
6.00
1.00