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A 250 m long train running at a speed of 100 km/h crosses another train, coming from the opposite direction at a speed of 62 km/h, in 10 seconds. What is the length of the second train?
200 m
240 m
230 m
270 m
200 m
Convert relative speed from km/h to m/s by multiplying by 185, then multiply by time to get the total length, and subtract the first train's length.
Length of the first train (L1) = 250 m, Speed of the first train (S1) = 100 km/h, Speed of the second train (S2) = 62 km/h coming from the opposite direction, Time taken to cross each other (t) = 10 seconds.
L1+L2=(S1+S2)×185×t
Convert relative speed from km/h to m/s by multiplying by 185, then multiply by time to get the total length, and subtract the first train's length.
Forgetting to add the two train lengths together or forgetting to convert the relative speed from km/h to m/s.
Step 1: Calculate Relative Speed
When two objects move in opposite directions, their relative speed is the sum of their individual speeds.
Srel=100+62=162 km/h
Step 2: Convert Relative Speed to m/s
Multiply the speed in km/h by 185 to convert it into meters per second.
Srel=162×185=45 m/s
Step 3: Calculate Total Distance Covered
The total distance covered while crossing is the sum of the lengths of both trains, which equals relative speed multiplied by time.
Dtotal=45 m/s×10 s=450 m
Step 4: Find Length of the Second Train
Subtract the length of the first train from the total distance to get the length of the second train (L2).
L2=450−250=200 m
A is correct because the calculated length of the second train is 200 m, which matches Option A.
In physics, relative motion problems involving trains, boats, or cars always require careful unit conversion and summing/subtracting speeds based on direction.
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