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.

Explanation

Rate at which the length of his shadow increases `=frac{{ds}}{{dt}}`.


In `triangle {ASB}, tan theta=frac{{AB}}{{AS}}=frac{6}{1+{s}}`


In `Delta {MSN}, tan theta=frac{{MN}}{{MS}}=frac{2}{{s}}`


From (1) and (2)


`frac{6}{1+s}=frac{2}{s}`


`Rightarrow 6 {s}=21+2 {s}`


`Rightarrow 4 {s}=21`


or `1=2 {s}`


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