A train 100m long travelling at 72 km/h overtakes another train travelling in the same direction at 54sec. Find the length of the second train
To find the length of the second train, we need to use the concept of relative speed.
Step 1: Convert the speed of the first train from km/h to m/s.
Speed (m/s) = Speed (km/h) × (1000/3600)
Speed (m/s) = 72 × (1000/3600)
Speed (m/s) = 20 m/s
Step 2: Calculate the relative speed of the first train with respect to the second train.
Relative Speed (m/s) = Speed of first train (m/s) - Speed of second train (m/s)
Relative Speed (m/s) = 20 m/s - 0 m/s
Relative Speed (m/s) = 20 m/s
Step 3: Calculate the time taken by the first train to overtake the second train.
Given, time taken = 54 seconds
Step 4: Use the formula: Relative Speed = Distance/Time
Relative Speed (m/s) = Distance (m) / Time (s)
Since the relative speed and time are given, we can find the distance traveled by the first train.
Distance (m) = Relative Speed (m/s) × Time (s)
Distance (m) = 20 m/s × 54 s
Distance (m) = 1080 m
Step 5: Subtract the length of the first train from the distance traveled by the first train to find the length of the second train.
Length of second train (m) = Distance traveled by first train (m) - Length of first train (m)
Length of second train (m) = 1080 m - 100 m
Length of second train (m) = 980 m
Therefore, the length of the second train is 980 meters.
To find the length of the second train, we can use the concept of relative speed.
Given:
Length of the first train = 100m
Speed of the first train = 72 km/h
Let's convert the speed of the train in m/s:
72 km/h * (1000m / 1 km) * (1 h / 3600s) = 20 m/s
We also know that the first train takes 54 seconds to overtake the second train.
Let's assume the length of the second train is "x" meters.
Now, we can calculate the relative speed between the two trains:
Relative speed = Speed of the first train - Speed of the second train
Relative speed = 20 m/s - 0 (as both the trains are moving in the same direction)
Relative speed = 20 m/s
Relative speed = Distance / Time
20 m/s = (100m + x) / 54s
Now, cross-multiplying:
20 * 54 = 100 + x
1080 = 100 + x
Subtracting 100 from both sides:
1080 - 100 = x
980 = x
Therefore, the length of the second train is 980 meters.