A 1.5 m tall boy is walking away from the base of a lamp post which is 12 m high, at the speed of 2.5 m/sec. Find the length of his shadow after 3 seconds.
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
Distance walked by boy in 3 sec = 2.5 × 3 = 7.5 m from the base of the lamp post.
Let the length of shadow = $x$ m.
Using similar triangles (lamp post and boy):
$$\frac{12}{1.5} = \frac{7.5 + x}{x}$$
$$8x = 7.5 + x$$
$$7x = 7.5$$
$$x = \frac{7.5}{7} = \frac{15}{14} \approx 1.07 \text{ m}$$
∴ Length of shadow after 3 seconds = $\dfrac{15}{14}$ m ≈ 1.07 m
Explanation
- The key step is setting up similar triangles: the lamp post (12 m) and the boy (1.5 m) are parallel verticals; their tips and the shadow tip are collinear, giving the ratio 12/1.5 = (total distance from post to shadow tip)/(shadow length).
- First find the distance of the boy from the post (speed × time = 7.5 m), then let shadow = $x$ so total = $7.5 + x$.
- Examiners award 1 mark for correct similar-triangle setup and 1 mark for correct final answer.