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

Ladder Length L (m)10.00

Bottom Speed dx/dt (m/s)2.00

Bottom Distance x for Focus (m)6.00

Animation Speed1.00

Show Instantaneous Rates

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