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Question

A man 1.6m tall walks at the rate of 0.5m/s away from a lamp post of 8 meters height. find the rate at which his shadow is increasing.

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Solution

Consider the fig,

Let x be the distance of the man from the pole at time t.
Let s be the length of the shadow at time t.

CEDAEB from AAA Postulate

CECD=AEAB

s1.6=x+s8

5s=x+s

s=14x

The man is walking at the speed of 0.5m/s

dxdt=0.5

Rate of change of length of the shadow is dsdt

=dsdx dxdt

=ddx(14x) 0.5

=14×0.5=0.25

Rate at which the shadow is increasing is 0.25 m/s

1168930_1028916_ans_1563d116a2ad4c378bb39cf2aca246a3.png

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