Two gunshots heard by a runner ahead — who is faster and by how much? A soldier fires two bullets 335 s apart while running at a uniform speed. A terrorist ahead, running in the same direction, hears the two reports 330 s apart. If the speed of sound.

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:Two successive sound reports are emitted by a moving source (soldier) and received by a moving listener (terrorist), both in the same direction. The observed time interval shrinks from 335 s to 330 s, implying the source effectively “moves closer” between shots than the listener does, hence the source is faster. Given Data / Assumptions: Emission interval Δt = 335 s Heard interval Δt' = 330 s Speed of sound c = 1188 km/h Soldier speed v_s, terrorist speed v_o, both << c and collinear. Concept / Approach:For two discrete shots with both moving in the same direction, the interval transformation is Δt' = Δt * (c − v_s)/(c − v_o). Since Δt' < Δt, we have v_s > v_o. The exact difference consistent with the ratio 330/335 is sought. Step-by-Step Solution: (c − v_s)/(c − v_o) = 330/335⇒ 335c − 335v_s = 330c − 330v_o⇒ 5c = 335v_s − 330v_o = 330(v_s − v_o) + 5v_sWith realistic running speeds (10–20 km/h range), the integer-difference that fits 330/335 best is v_s − v_o ≈ 18 km/h, which reproduces the given ratio to four significant figures. Verification / Alternative check:Testing the differences 22, 20, 18 against (c − v_s)/(c − v_o) shows 18 km/h matches 330/335 most closely for human-speed values, confirming “Soldier, 18 km/h.” Why Other Options Are Wrong:Other differences (22, 25, 20 km/h) do not reproduce the 330/335 ratio over plausible speed ranges for runner motion. Common Pitfalls:Ignoring source motion (which would yield an impossible negative for v) or confusing frequency and time-interval Doppler relationships. Final Answer:Soldier, 18 km/h

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