MHT CET · Maths · Application of Derivatives
A ladder 5 m long rests against a vertical wall. If its top slides downwards at the rate of \(10 \mathrm{~cm} / \mathrm{sec}\)., then the foot of the ladder is sliding at the rate of _______ \(\mathrm{m} / \mathrm{sec}\), when it is 4 m away from the wall.
- A 0.75
- B 7.5
- C 0.0075
- D 0.075
Answer & Solution
Correct Answer
(D) 0.075
Step-by-step Solution
Detailed explanation
According to the figure, \(x^2+y^2=25\)
At \(x=4, y=3\)
Differentiating (i) with respect to ' \(t\) ', we get
\(\begin{aligned}
& 2 x \frac{\mathrm{~d} x}{\mathrm{dt}}+2 y \cdot \frac{\mathrm{~d} y}{\mathrm{dt}}=0 \\
& x \frac{\mathrm{~d} x}{\mathrm{dt}}=-y \frac{\mathrm{~d} y}{\mathrm{dt}} \\
& \frac{\mathrm{~d} x}{\mathrm{dt}}=\frac{-y}{x} \frac{\mathrm{~d} y}{\mathrm{dt}}=\frac{-3}{4} \times(-0.1)=0.075
\end{aligned}\)
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