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Two trains 120 m and 80 m in length are running in opposite directions with velocities 42 kmph and 30 kmph. In what time they will cross each other?
- a)15 sec
- b)20 sec
- c)10 sec
- d)12 sec
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two trains 120 m and 80 m in length are running in opposite directions...
Relative velocity of one train w.r. to other
= 42 – (-30) (as both are in opposite direction)
= 72 kmph = 20 m/sec
Total distance to be covered by each train to cross other train = 120 + 80 = 200 m
Time taken by each train to cross other train = 200/20 = 10 sec
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Two trains 120 m and 80 m in length are running in opposite directions...
Given:
- Length of first train (A) = 120 m
- Length of second train (B) = 80 m
- Velocity of first train (A) = 42 km/h
- Velocity of second train (B) = 30 km/h
To find:
- Time taken for the two trains to cross each other
Explanation:
When two objects are moving towards each other, the distance between them decreases at a rate equal to the sum of their velocities.
Approach:
1. Convert the velocities of the trains from km/h to m/s.
2. Calculate the relative velocity of the two trains.
3. Use the formula: Time = Distance / Relative velocity to find the time taken for the two trains to cross each other.
Calculations:
1. Conversion of velocities from km/h to m/s:
- Velocity of first train (A) = 42 km/h = (42 * 1000) / (60 * 60) = 11.67 m/s
- Velocity of second train (B) = 30 km/h = (30 * 1000) / (60 * 60) = 8.33 m/s
2. Calculation of relative velocity:
- Relative velocity = Velocity of first train (A) + Velocity of second train (B)
- Relative velocity = 11.67 m/s + 8.33 m/s = 20 m/s
3. Calculation of time:
- Distance = Length of first train (A) + Length of second train (B)
- Distance = 120 m + 80 m = 200 m
- Time = Distance / Relative velocity
- Time = 200 m / 20 m/s = 10 s
Answer:
The two trains will cross each other in 10 seconds. Therefore, the correct option is c) 10 sec.
- Length of first train (A) = 120 m
- Length of second train (B) = 80 m
- Velocity of first train (A) = 42 km/h
- Velocity of second train (B) = 30 km/h
To find:
- Time taken for the two trains to cross each other
Explanation:
When two objects are moving towards each other, the distance between them decreases at a rate equal to the sum of their velocities.
Approach:
1. Convert the velocities of the trains from km/h to m/s.
2. Calculate the relative velocity of the two trains.
3. Use the formula: Time = Distance / Relative velocity to find the time taken for the two trains to cross each other.
Calculations:
1. Conversion of velocities from km/h to m/s:
- Velocity of first train (A) = 42 km/h = (42 * 1000) / (60 * 60) = 11.67 m/s
- Velocity of second train (B) = 30 km/h = (30 * 1000) / (60 * 60) = 8.33 m/s
2. Calculation of relative velocity:
- Relative velocity = Velocity of first train (A) + Velocity of second train (B)
- Relative velocity = 11.67 m/s + 8.33 m/s = 20 m/s
3. Calculation of time:
- Distance = Length of first train (A) + Length of second train (B)
- Distance = 120 m + 80 m = 200 m
- Time = Distance / Relative velocity
- Time = 200 m / 20 m/s = 10 s
Answer:
The two trains will cross each other in 10 seconds. Therefore, the correct option is c) 10 sec.
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Two trains 120 m and 80 m in length are running in opposite directions with velocities 42 kmph and 30 kmph. In what time they will cross each other?a)15 secb)20 secc)10 secd)12 secCorrect answer is option 'C'. Can you explain this answer?
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