JEE Advanced 2023 Paper 1 · Q12 · Work-Energy-Power
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$^{-1}$.
Reveal answer + step-by-step solution
Correct answer:40
Solution
By similar triangles, if person is at distance $x_1$ from lamp post and shadow tip is at $x_2$ from lamp post, $x_2/x_1 = 4/(4-1.6) = 4/2.4 = 5/3$. So $dx_2/dt = (5/3)dx_1/dt = (5/3)(60) = 100$ cm/s (shadow tip's speed in ground frame). Speed relative to person = $100 - 60 = 40$ cm/s.
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