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A Man 2 Metres Tall Walks Away from a Lamp Post 5 Metres Height at the Rate of 4.8 Km/Hr. the Rate of Increase of the Length of His Shadow is (A) 1.6 Km/Hr (B) 6.3 Km/Hr(C) 5 Km/Hr (D) 3.2 Km/Hr - Mathematics

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Question

A man 2 metres tall walks away from a lamp post 5 metres height at the rate of 4.8 km/hr. The rate of increase of the length of his shadow is

Options
  • 1.6 km/hr

  • 6.3 km/hr

  •  5 km/hr

  • 3.2 km/hr

Solution

Let AB be the lamp post. Suppose at any time t, the man CD be at a distance of x km from the lamp post and y m be the length of his shadow CE.

\[\text { Since triangles ABE and CDE are similar }, \]

\[\frac{AB}{CD} = \frac{AE}{CE}\]

\[\Rightarrow \frac{5}{2} = \frac{x + y}{y}\]

\[ \Rightarrow \frac{x}{y} = \frac{5}{2} - 1\]

\[ \Rightarrow \frac{x}{y} = \frac{3}{2}\]

\[ \Rightarrow y = \frac{2}{3}x\]

\[ \Rightarrow \frac{dy}{dt} = \frac{2}{3}\left( \frac{dx}{dt} \right)\]

\[ \Rightarrow \frac{dy}{dt} = \frac{2}{3} \times 4 . 8\]

\[ \Rightarrow \frac{dy}{dt} = 3 . 2 \ km/hr\]

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 13: Derivative as a Rate Measurer
Q: 22 | Page no. 26
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A Man 2 Metres Tall Walks Away from a Lamp Post 5 Metres Height at the Rate of 4.8 Km/Hr. the Rate of Increase of the Length of His Shadow is (A) 1.6 Km/Hr (B) 6.3 Km/Hr(C) 5 Km/Hr (D) 3.2 Km/Hr Concept: Rate of Change of Bodies Or Quantities.
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