Academic session 2026-27, Chapter 6 in the current curriculum.
Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter Application of Derivatives. This page offers a step-by-step solution to the specific question from Exercise 1, Question 10:
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?
. With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.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?
Let y m be the height of the wall at which the ladder touches. Also, let the foot of the ladder be x maway from the wall.
Then, by Pythagoras theorem, we have:
x2 + y2 = 25 [Length of the ladder = 5 m]
\begin{align}\Rightarrow y = \sqrt{25 - x^2}\end{align}
Then, the rate of change of height (y) with respect to time (t) is given by,
\begin{align}\frac{dy}{dx} = \frac{-x}{\sqrt{25 - x^2}}.\frac{dx}{dt}\end{align}
It is given that
\begin{align}\frac{dx}{dt}= 2 \; cm/s.\end{align}
\begin{align}\therefore\frac{dy}{dt} = \frac{-2x}{\sqrt{25 - x^2}}\end{align}
Now, when x = 4 m, we have:
\begin{align}\therefore\frac{dy}{dt} = \frac{-2 \times 4}{\sqrt{25 - 4^2}}=-\frac{8}{3}\end{align}
Hence, the height of the ladder on the wall is decreasing at the rate of
\begin{align}\frac{8}{3}\end{align}
NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:
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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 10: A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, aw....
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Comments
Thank u so much
need to change the units?
how do u got dy/dx