MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A 15-ft ladder rests against a vertical wall. The top of the ladder slides down the wall at a constant rate of 2 ft/s. At the instant when the top of the ladder is 9 ft above the ground, answer the following.
(a) Determine the rate at which the foot of the ladder is moving away from the wall.
(b) Compute the instantaneous rate of change of the angle θ between the ladder and the ground at that same instant. Express your answer in radians per second.
(c) Decide whether the speed of the foot of the ladder is increasing or decreasing as the ladder continues to slide. Support your conclusion with mathematical reasoning.