A ladder m long rests against a vertical wall

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A ladder

10

m long rests against a vertical wall. The foot of the ladder is pulled away from the wall along level ground. (i) Let

x

m be the distance of the foot from the wall and

y

m the height of the top above the ground. Write the equation connecting

x

and

y

. (ii) Obtain a formula for

\dfrac{dy}{dt}

in terms of

x

y

and

\dfrac{dx}{dt}

. (iii) When the foot is

6

m from the wall and moving away at

0.5\,\text{m s}^{-1}

, determine the speed at which the top is sliding down the wall. (iv) At the same instant, find the rate of change of the area of the right-angled triangle formed by the ladder, the wall and the ground.

Related theory

Pythagoras' Theorem
Triangle Properties
Related Rates

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