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. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

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. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

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

Answer: D) 8/3 cm/s

Explanation: Let x be distance from wall and y be height. x² + y² = 25. Differentiating w.r.t t: 2x(dx/dt) + 2y(dy/dt) = 0. When x=4, y=3. 4(2) + 3(dy/dt) = 0, giving dy/dt = -8/3. Decrease rate is 8/3 cm/s.