COMEDK · Maths · 27. Application of Derivatives

A ladders \(5 \mathrm{~m}\) long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of \(2 \mathrm{~m} / \mathrm{sec}\). The speed at which its height on the wall decreases when the foot of the ladder is \(4 \mathrm{~m}\) away from the wall is

A \(\frac{3}{8} \mathrm{~m} / \mathrm{sec}\)
B \(\frac{8}{3} \mathrm{~m} / \mathrm{sec}\)
C \(\frac{5}{3} \mathrm{~m} / \mathrm{sec}\)
D \(\frac{2}{3} \mathrm{~m} / \mathrm{sec}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{8}{3} \mathrm{~m} / \mathrm{sec}\)

Step-by-step Solution

Detailed explanation

Let \(A B\) be the ladder of length \(5 \mathrm{~m}\). We are given, \(\frac{d x}{d t}=2 \mathrm{~m} / \mathrm{sec}\) In \(\triangle A B C\) \[ \begin{aligned} & A B^{2}=A C^{2}+B C^{2} \\ \Rightarrow \quad &(5)^{2}=x^{2}+h^{2} \quad \text{...(i)} \end{aligned} \]…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From COMEDK

Explore more questions on app