Falling Ladder: Related Rates Question
- Tim Brzezinski
Question (1) taken from Stewart's Calculus (Early Trancendentals) text: 1) If the ladder is moving away from the wall at 1 ft/sec, how fast is h changing at the exact instant when x = 6 ft? 2) Why is dh/dt < 0 (regardless of the point at which the ladder meets the floor)? Explain. 3) At what instance does the absolute value of dh/dt the greatest? How is this made apparent? 4) At what instance does the absolute value of dh/dt the least? How is this made apparent? 5) Is there ever a time for which the absolute value of dx/dt = the absolute value of dh/dt? If not, explain why. If so, determine the values of h and x for which this occurs.