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

पर्याय

• 1.6 km/hr

• 6.3 km/hr

•  5 km/hr

• 3.2 km/hr

Answer 1

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.

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

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

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

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

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

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

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

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

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