Example 43
A
man of height 180 cm is moving away form a lamppost at the rate
of 1.2/sec. If the height of the lamppost is 4.5 m. Find the rate
at which the shadow is lengthening by the rate at which its tip
is moving away from the lamppost.?
Solution :
AB = lamppost,
AB = 4.5 cm
CD = Man.
CD = 180 cm =1.8 m
DE = Shadow
and distance of the tip E of the shadow from the
pole = BE
Let BD = X and DE = Y
then BE = X + Y
Now D ABE ~ D CDE ... (By AA test for similar triangles)
\
\
\
\
\
\
Differentiating w. r. to ’ t ’.
\ The
shadow is lengthening at the rate 0.8 m / sec.
Also BE = X + Y
\ Differentiating w. r. to ’ t’
\ The rate at which
the tip of the shadow is moving away from the lamppost is 2 m/sec.
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