JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Kinematics

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A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is

60 cm s^{- 1}

, the speed of the tip of the person's shadow on the ground with respect to the person is ____

cm s^{- 1}

Answer: 40

Solution

Let the person be at distance

y

from the lamp post, and the shadow tip at distance

x

from the person.

By similar triangles:

\frac{4}{y + x} = \frac{1.6}{x}

4 x = 1.6 (y + x)

4 x = 1.6 y + 1.6 x

2.4 x = 1.6 y

x = \frac{2}{3} y

Differentiating:

\frac{d x}{d t} = \frac{2}{3} \frac{d y}{d t}

Given

\frac{d y}{d t} = 60

cm/s:

\frac{d x}{d t} = \frac{2}{3} \times 60 = 40

cm/s

This is the speed of the shadow tip relative to the person.

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Integer answer

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