एक 800 मीटर लम्बी ट्रेन, 78 किमी/घंटे की गति से चल रही है यदि यह एक पुल को 1 मिनट में पार कर जाती है तो पुल की लम्बाई (मीटर) में ज्ञात कीजिये?a)77200 b)500c)1300 d)13Correct answer is option 'B'. Can you explain this answer?

Question

एक  800 मीटर लम्बी ट्रेन, 78 किमी/घंटे की गति से चल रही है यदि यह एक पुल को  1 मिनट में पार कर जाती है तो पुल की लम्बाई (मीटर) में ज्ञात कीजिये?a)77200 b)500c)1300  d)13Correct answer is option 'B'. Can you explain this answer?

Answer

Problem Solving:
To solve this problem, we need to use the formula of relative speed. The relative speed is the difference between the speeds of two objects moving in the same direction or opposite directions.

Relative speed = Speed of the train - Speed of the object (here, the object is the bridge).

Given:
Speed of the train = 78 km/h
Length of the train = 800 m
Time taken to cross the bridge = 1 minute

First, we need to convert the speed of the train from km/h to m/s.

1 km/h = 1000 m/3600 s = 5/18 m/s

Therefore, the speed of the train = 78 × 5/18 = 21.67 m/s

Next, we need to find the length of the bridge.

Length of the train + Length of the bridge = Distance covered in 1 minute

As the train crosses the bridge, it covers the length of the train and the length of the bridge. This distance is equal to the length of the train plus the length of the bridge.

Distance = Speed × Time

Here, the speed is the relative speed between the train and the bridge, and the time is 1 minute or 60 seconds.

Relative speed = Speed of the train - Speed of the bridge (which is at rest)

Relative speed = 21.67 - 0 = 21.67 m/s

Distance = Relative speed × Time
Distance = 21.67 × 60 = 1300.2 m

Length of the train + Length of the bridge = 1300.2 m

Length of the bridge = 1300.2 - 800 = 500.2 m

Therefore, the length of the bridge is 500 meters.

Answer: Option B (500)

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