Application of Derivatives
Rate of Change
Premium Question
Grade 12
Question:
A ladder 5 m long is leaning against a wall. The bottom is being pulled away from the wall at 2 m/s. How fast is the top of the ladder sliding down the wall when the bottom is 4 m from the wall?
(1) $\frac{8}{3} \text{ m/s}$
(2) $\frac{3}{8} \text{ m/s}$
(3) $\frac{6}{5} \text{ m/s}$
(4) $\frac{5}{6} \text{ m/s}$
Step-by-Step Solution
Key Concept: Write the Pythagorean relation $x^2 + y^2 = 25$ connecting the distances $x$ (bottom from wall) and $y$ (top from ground), then differentiate both sides with respect to time.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)