A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 2 cm/s. The rate at which the height on the wall is decreasing when the foot of the ladder is 4 m away from the wall is:

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of 2 cm/s. The rate at which the height on the wall is decreasing when the foot of the ladder is 4 m away from the wall is:

• A. 8/3 cm/s
• B. 3/8 cm/s
• C. 3/4 cm/s
• D. 4/3 cm/s

Answer: A) 8/3 cm/s

Explanation: x² + y² = 25. 2x dx/dt + 2y dy/dt = 0. x = 4, dx/dt = 0.02 m/s. y = 3. dy/dt = −(x/y) dx/dt = −(4/3)(0.02) = −0.08/3 m/s = −8/3 cm/s. Rate of decrease = 8/3 cm/s.