MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A 13-ft ladder leans against a vertical wall. When the foot of the ladder is 5 ft from the wall, it begins to slide directly away from the wall at a constant rate of 4 in/s. Assume the ladder maintains contact with both the wall and the ground.
(a) Determine the rate (in ft/s) at which the top of the ladder is descending at the instant when the foot of the ladder is 5 ft from the wall.
(b) At the same instant, find the rate (in rad/s) at which the angle between the ladder and the ground is changing.
(c) State whether this angle is increasing or decreasing at that instant and justify your answer numerically.