A man - 2 m tall- walks at the rate of 1 23 m-s towards a street light which is 5 13m above the ground- The rate at which the shadow of his tip of head is moving towards the street light will be

Given; dsdt = 1 23 = 53 m/s Let T be the tip of shadow. s +l(5 nbsp; 13) = l2 ⇒3 (s + l)16 = l2⇒ 3s = 5l ∴ 3 dsdt = 5 dldt⇒dldt = 1 m/s So, rate at which ...

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A man , 2 m t...

Question

A man , $2 m$ tall, walks at the rate of $1 \frac{2}{3} m / s$ towards a street light which is $5 \frac{1}{3} m$ above the ground. The rate at which the shadow of his tip of head is moving towards the street light will be

\frac{11}{3} m / s

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\frac{8}{3} m / s

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\frac{2}{3} m / s

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\frac{4}{3} m / s

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Solution

The correct option is B $\frac{8}{3} m / s$
Given; $\frac{d s}{d t} = - 1 \frac{2}{3} = - \frac{5}{3} m / s$
Let $T$ be the tip of shadow.
$\frac{s + l}{(5 \frac{1}{3})} = \frac{l}{2}$
$\Rightarrow \frac{3 (s + l)}{16} = \frac{l}{2} \Rightarrow 3 s = 5 l$
$∴ 3 \frac{d s}{d t} = 5 \frac{d l}{d t} \Rightarrow \frac{d l}{d t} = - 1 m / s$
So, rate at which shadow of tip of head is moving $= \frac{d s}{d t} + \frac{d l}{d t} = \frac{- 8}{3} m / s$

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Similar questions

Q. A man,

2 m

tall, walks ar the rate of

1 \frac{2}{3} m / s

towards a street light which is

5 \frac{1}{3} m

above the ground. At what rates is the tip of his shadow moving ? At what is the length of the shadow changing when he is

3 \frac{1}{3} m

from the base of the light?

A man , 2 m tall, walks at the rate of $1 \frac{2}{3}$ m/s towards a street light which is $5 \frac{1}{3}$ m above the ground. At what rate is the tip of his shadow moving and at what rate is the length of the shadow changing when he is $3 \frac{1}{3}$ m from the base of the light?