A ladder slides down a vertical wall while its base moves horizontally away from the wall

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

Problem

5\,\text{m}

ladder slides down a vertical wall while its base moves horizontally away from the wall. Let

x(t)

be the distance from the wall to the base and

y(t)

the height of the top above the floor, with

x^{2}+y^{2}=25

at all times. Derive an expression for

\displaystyle \frac{dy}{dt}

in terms of

x

y

, and

\displaystyle \frac{dx}{dt}