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:
This question is important because it tests key concepts from the NCERT syllabus and is frequently asked in CBSE exams.
This question is based on core NCERT concepts explained in the chapter and should be revised thoroughly before exams.
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{al...
Step-by-step explanation:
• 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:
Students often lose marks by skipping steps, writing incomplete explanations, or misunderstanding keywords used in the question.
Stay updated with our latest educational content and study tips
Parent-Teacher Meetings (PTMs) are more than quick updates on marks — they’re a chance to build a real partnership between home and school. A good Parent-Teacher Meeting conversation helps parents see beyond grades. It opens up insights about a child’s strengths, struggles, emotions and even hidden talents. When parents participate actively, they don’t just track […]
Read More
In today’s world of endless information , knowing how to think is more important than knowing what to think . From school projects to real – life decisions , critical thinking helps students question ideas , analyze facts and form logical conclusions . But what exactly does critical thinking mean ? Simply put , it’s […]
Read More
Every student dreams of better grades , stronger focus and more study time – but the real challenge isn’t starting, it’s staying consistent . Building productive study habits is not about studying all day , it’s about studying smart . In today’s fast – paced digital world, distractions are everywhere – from endless phone notifications […]
Read More
Online gaming has rapidly become one of the most popular pastimes among children. Whether it’s multiplayer mobile games , PC adventures or console challenges , kids are spending more time than ever in the virtual world . On the surface, gaming seems entertaining and even educational – improving hand- eye coordination , teamwork and problem […]
Read More
Student Discussion
ADD NEW COMMENT