A man 2 metres high walks at a uniform speed of 5 km/hr away from a lamp-post 6 metres high. Find the rate at which the length of his shadow increases.

Options

A. `2` k.m/hr
B. `3.5` k.m/hr
C. `2.5` k.m/hr
D. `3` k.m/hr

Answer

C

Explanation

Let `AB` be the lamp post. let at any time `t`, the man `CD` be at a distance o `x` km from the lamp post and `y` m be the length of his shadow `CE`.
`triangle ABE ` and `CDE` are similar

`frac{A B}{C D}=frac{A E}{C E} `
`
Rightarrow frac{6}{2}=frac{x+y}{y} `
`
Rightarrow frac{x}{y}=frac{6}{2}-1=2`
`
Rightarrow frac{d y}{d t}=frac{1}{2} frac{d x}{d t} `
`
Rightarrow frac{d y}{d t}=frac{1}{2}(6) `
`
Rightarrow frac{d y}{d t}=3 ({km} / (hr))`
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