Train Crossing Time Ratio – Relative Motion in Same and Opposite Directions | JEE Physics

 

🚆 Train Crossing Time Ratio – Relative Motion | Speed, Distance & Time | JEE Physics | Doubtify JEE

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💡 Question:

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr.
Find the ratio of times taken by the passenger train to completely cross the freight train when:

(i) They are moving in the same direction, and
(ii) They are moving in opposite directions.

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🖼️ Question Image:

🧠 Solution (Image):

✍️ Step-by-Step Explanation:

This is a classic relative motion problem, frequently asked in JEE Mains. We are to find the time taken to cross and the ratio of times under two different cases.

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👉 Given:

• Length of passenger train = 60 m

• Length of freight train = 120 m

• Speed of passenger train = 80 km/h = 22.22 m/s

• Speed of freight train = 30 km/h = 8.33 m/s

Total length to be crossed = 60 + 120 = 180 m

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Case 1: Same Direction

Relative speed = 22.22 – 8.33 = 13.89 m/s
Time = Distance / Speed = 180 / 13.89 ≈ 12.96 s

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Case 2: Opposite Direction

Relative speed = 22.22 + 8.33 = 30.55 m/s
Time = 180 / 30.55 ≈ 5.89 s

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✅ Ratio of Time (Same Dir / Opposite Dir):

= 12.96 / 5.89 ≈ 2.2 : 1

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🎥 Video Solution:

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🔍 Why This Question Is Important:

• Builds conceptual clarity in relative motion

• Combines train crossing formula with unit conversion

• Highly relevant for JEE Mains MCQs

• Improves speed in solving real-world speed-distance problems

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🧠 Pro Tip:

Always convert speeds to m/s before applying formulas.
Relative speed is the key in problems involving two moving bodies.

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