A man sitting in a train which is travelling at 50 km ph observes that a goods…
2023
A man sitting in a train which is travelling at 50 km ph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
Answer: C. 62 km ph — ConceptWhen two bodies move in opposite directions, their relative speed is the sum of their individual speeds. A train of length L passing an observer, who…
- A.
60 km ph
- B.
65 km ph
- C.
62 km ph
- D.
64 km ph
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
When two bodies move in opposite directions, their relative speed is the sum of their individual speeds. A train of length L passing an observer, who counts as a point object, must cover exactly L at that relative speed, so time taken = L / relative speed. The unit bridge between the two systems is 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h.
Application
The observer is a single person, so the distance the goods train covers relative to him is its own full length, 280 m.
Relative speed = distance / time = 280 m / 9 s = 280/9 m/s.
Convert to km/h: 280/9 × 18/5 = 5040/45 = 112 km/h.
The two trains run in opposite directions, so the relative speed is the sum: speed of goods train + 50 km/h = 112 km/h.
Speed of the goods train = 112 - 50 = 62 km/h.
Cross-check
Adding back: 62 + 50 = 112 km/h, which is 112 × 5/18 = 280/9 m/s, about 31.11 m/s. The time to cover 280 m at that rate is 280 / (280/9) = 9 seconds, exactly the observation given. Note that the stated direction is load-bearing: had the trains run in the same direction the relative speed would be a difference, and 280/9 m/s would instead force a goods-train speed of 162 km/h.