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Question

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.

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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.


Since triangles ABE and CDE are similar,ABCD=AECE62=x+yy3y=x+yx=2ydxdt=2dydtdydt=12dxdtdydt=125 dxdt=5dydt=52 km/hr

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