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explain solution RD Sharma class 12 chapter Derivative As a Rate Measure exercise 12.2 question 20 maths

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Answer: \frac{d y}{d t}=\frac{3 k m}{h r}

Hint: The rate at which the length of the man’s shadow increases will be \frac{d y}{d t}

Given: A man 2 m tall walks at a speed of 6 km/hr away from a source of light that is 6 m above the ground.

Solution: Let AB  the lamp post and let at any time t .The man CD be at a distance of x km from the lamp post and y be the length of his shadow

Since triangle \Delta ABE and \Delta CDE are similar

\begin{aligned} &\frac{A B}{C D}=\frac{B E}{D E} \\\\ &\frac{6}{2}=\frac{x+y}{y} \\\\ &\frac{x}{y}=\frac{6}{2}-1=2 \end{aligned}

Let’s take derivative with respect to time both side

\frac{d y}{d t}=\frac{1}{2} \times \frac{d x}{d t}

Let’s put value of \frac{d x}{d t}=6 \mathrm{~km}(\text { given })

\frac{d y}{d t}=\frac{1}{2} \times 6=3 \mathrm{~km} / \mathrm{hr}

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