A ship travelling towards a cliff receives the echo of its whistle after 3.5 seconds. A short while later, it…

Analyze the question

A ship sends out a whistle sound, which travels to the cliff and back (an echo). The echo time changes from 3.5 s to 2.5 s, and we need the distance the ship moved closer to the cliff.

Concept

An echo involves the sound travelling to the cliff and back, so:

2d = v × t, which gives d = vt / 2

Solution

• First position: d₁ = (250 × 3.5) / 2 = 875 / 2 = 437.5 m
• Second position: d₂ = (250 × 2.5) / 2 = 625 / 2 = 312.5 m

Distance moved closer:

d₁ − d₂ = 437.5 − 312.5 = 125 m

Or in one step: Δd = v(Δt) / 2 = 250 × (3.5 − 2.5) / 2 = 250 × 1 / 2 = 125 m

Answer: 125 m, which is option D.

Tip: In echo questions, always divide by 2, because the sound covers the distance twice (going and returning). For "how much closer" questions, subtract the two times first, then use Δd = v × Δt / 2. A common mistake is forgetting to halve, which would give 250 m, and that is not among the options.