MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A 13-ft ladder rests against a vertical wall. The foot of the ladder slides horizontally away from the wall at a constant rate of 1.5 ft/s. Which of the following statements best describes the vertical motion of the top of the ladder as the foot moves from very close to the wall to farther away?
(a) The top moves downward at a constant 1.5 ft/s for all positions.
(b) The top first rises and then falls once the foot has moved more than half the ladder’s length from the wall.
(c) The top moves downward, and its speed increases as the foot moves farther from the wall.
(d) The top moves downward, and its speed decreases as the foot moves farther from the wall.