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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The rate of increase of length of the shadow of a man $2$ meters high, due to a lamp at $10$ meters height, when he is moving away from it at $2 \text{ m/sec}$ is
Solution
Let $x =$ distance of man from lampLet $y =$ length of shadow
By similar triangles:
$\dfrac{10}{x+y} = \dfrac{2}{y}$ Cross-multiply:
$10y = 2(x+y)$
$10y = 2x + 2y$
$8y = 2x$
$y = \dfrac{x}{4}$
Differentiate w.r.t time $t$:
$\dfrac{dy}{dt} = \dfrac{1}{4}\dfrac{dx}{dt}$
Given $\dfrac{dx}{dt} = 2$ m/sec
:
$\dfrac{dy}{dt} = \dfrac{1}{4} \times 2 = \dfrac{1}{2}$
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