JEE Advanced 2023 · Paper 1 · Physics Q12

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PhysicsInteger+4Question 29 of 51

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 $60\ \mathrm{cm\,s^{-1}}$ , the speed of the tip of the person's shadow on the ground with respect to the person is _____ $\mathrm{cm\,s^{-1}}$ .

Your answer

Answer and worked solution

Official answer: 40

Let $x$ be the person's distance from the post and $s$ the distance of the shadow tip from the post.

Similar triangles.
$\frac{s}{4}=\frac{s-x}{1.6}\implies s=\frac{4}{2.4}x=\frac53x.$

Speeds. The tip moves at $\frac53\times60=100$ cm/s. Relative to the person this is $100-60=40$ cm/s.

Topics:Relative velocity Motion in a straight line

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