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If a train takes 1.75 sec to cross a telegraph pole and 1.5 sec to a cyclist travelling in opposite direction at 10 m per second, then the length of the train is:
- a)135 m
- b)125 m
- c)115 m
- d)105 m
Correct answer is option 'D'. Can you explain this answer?
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If a train takes 1.75 sec to cross a telegraph pole and 1.5 sec to a ...
Spouse speed of train = x m/s
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or length of train = I m
Time taken by trains to cross a telegraph cost
Using (i) and (ii)
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If a train takes 1.75 sec to cross a telegraph pole and 1.5 sec to a ...
Given:
- Time taken by the train to cross a telegraph pole = 1.75 sec
- Time taken by the train to cross a cyclist traveling in the opposite direction = 1.5 sec
- Speed of the cyclist = 10 m/s
To find:
The length of the train
Assumptions:
- The length of the telegraph pole is negligible compared to the length of the train.
- The time taken to cross the cyclist is the same as the time taken to cross the train completely.
Approach:
We can use the formula for speed, distance, and time to solve this problem. The formula is:
Speed = Distance / Time
Solution:
Let's denote the length of the train by 'L' meters.
1. Time taken to cross the telegraph pole:
The train takes 1.75 seconds to cross the telegraph pole. Since the length of the telegraph pole is negligible, the distance covered by the train in 1.75 seconds is equal to the length of the train.
So, the distance covered = L meters.
2. Time taken to cross the cyclist:
The train takes 1.5 seconds to cross the cyclist traveling in the opposite direction. In this case, the relative speed between the train and the cyclist is the sum of their speeds.
Relative speed = Speed of the train + Speed of the cyclist
Relative speed = 0 + 10 m/s (as they are traveling in opposite directions)
Distance covered = Relative speed × Time taken
Distance covered = 10 × 1.5 = 15 meters
3. Equating the distances covered in both cases:
Since the distance covered by the train in both cases should be the same, we equate the distances:
L = 15 meters
4. Finding the length of the train:
Therefore, the length of the train is 15 meters, which corresponds to option 'D'.
Answer:
The length of the train is 105 meters (option 'D').
- Time taken by the train to cross a telegraph pole = 1.75 sec
- Time taken by the train to cross a cyclist traveling in the opposite direction = 1.5 sec
- Speed of the cyclist = 10 m/s
To find:
The length of the train
Assumptions:
- The length of the telegraph pole is negligible compared to the length of the train.
- The time taken to cross the cyclist is the same as the time taken to cross the train completely.
Approach:
We can use the formula for speed, distance, and time to solve this problem. The formula is:
Speed = Distance / Time
Solution:
Let's denote the length of the train by 'L' meters.
1. Time taken to cross the telegraph pole:
The train takes 1.75 seconds to cross the telegraph pole. Since the length of the telegraph pole is negligible, the distance covered by the train in 1.75 seconds is equal to the length of the train.
So, the distance covered = L meters.
2. Time taken to cross the cyclist:
The train takes 1.5 seconds to cross the cyclist traveling in the opposite direction. In this case, the relative speed between the train and the cyclist is the sum of their speeds.
Relative speed = Speed of the train + Speed of the cyclist
Relative speed = 0 + 10 m/s (as they are traveling in opposite directions)
Distance covered = Relative speed × Time taken
Distance covered = 10 × 1.5 = 15 meters
3. Equating the distances covered in both cases:
Since the distance covered by the train in both cases should be the same, we equate the distances:
L = 15 meters
4. Finding the length of the train:
Therefore, the length of the train is 15 meters, which corresponds to option 'D'.
Answer:
The length of the train is 105 meters (option 'D').
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If a train takes 1.75 sec to cross a telegraph pole and 1.5 sec to a cyclist travelling in opposite direction at 10 m per second, then the length of the train is:a)135 mb)125 mc)115 md)105 mCorrect answer is option 'D'. Can you explain this answer?
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