Shadows Part-2

Calculus Level 2

A person of height 180 cm starts from a lamp post of height 450 cm and walks at a constant rate of 4 km/hr. The rate at which his shadow increases is

6 km/hr 4 km/hr 8/3 km/hr 2 km/hr

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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1 solution

By similar triangles, we have

y 180 = x 270 \dfrac{y}{180}=\dfrac{x}{270}

y = 180 270 x y=\dfrac{180}{270}x

Differentiate both sides with respect to t t .

d y d t = 180 270 d x d t = 180 270 ( 4 ) = 8 3 k p h \dfrac{dy}{dt}=\dfrac{180}{270}\dfrac{dx}{dt}=\dfrac{180}{270}(4)=\dfrac{8}{3}~kph

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