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  4. A man of height 'h' is walking away from a street lamp with a constant speed 'v'. The height of the street lamp is 3h. The rate at which of the length of the man's shadow is increasing when he is at a distance 10 h from the base of the street lamp is:

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Q. A man of height 'h' is walking away from a street lamp with a constant speed 'v'. The height of the street lamp is $3h$. The rate at which of the length of the man's shadow is increasing when he is at a distance $10 h$ from the base of the street lamp is:

Ray Optics and Optical Instruments

Solution:

image
$\frac{3 h-h}{y}=\frac{h}{x}$
$\Rightarrow \frac{2 h}{y}=\frac{h}{x}$
$x=\frac{y}{2} $
$\Rightarrow \frac{d x}{d t}=\frac{1}{2} \frac{d y}{d t}$
$v _{\text {shodow }}=\frac{ v }{2}$