A 15-ft ladder slides so that its foot moves away from a vertical wall at 3 ft/s

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A 15-ft ladder slides so that its foot moves away from a vertical wall at 3 ft/s. What is the rate of change of the angle

\theta

between the ladder and the ground when the foot of the ladder is 9 ft from the wall? (a)

-\dfrac{1}{6}\text{ rad/s}

(b)

+\dfrac{1}{4}\text{ rad/s}

(c)

-\dfrac{1}{4}\text{ rad/s}

(d)

-\dfrac{1}{3}\text{ rad/s}