A ladder of fixed length leans against a vertical wall

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A ladder of fixed length

L

leans against a vertical wall, forming an angle

\theta

(in radians) with the horizontal ground. The base is moving horizontally so that

\dfrac{dx}{dt}

is known at a particular instant, where

x

is the horizontal distance from the wall. Derive an expression for

\dfrac{d\theta}{dt}

in terms of

x

L

, and

\dfrac{dx}{dt}