A person of height m is walking away from a lamp post of height 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 p

Question

A person of height  m is walking away from a lamp post of height  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 , the speed of the tip of the person’s shadow on the ground with respect to the person is  cm s⁻¹.

Canvas Classes · Accepted Answer

🎯
- Lamp post  m, person  m, walking at  cm/s.
- Find the speed of the shadow's tip relative to the person.

💡 Similar triangles fix the tip's position as a multiple of the person's distance; then differentiate.

✏️
Let  = person's distance from the post,  = shadow length. Similar triangles:

Tip position

Relative to the person:

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