To determine the length of the train, we can start by converting the speed from km/h to m/s.
Given: Speed of the train = 120 km/h Time taken to cross the tunnel = 5 minutes
Converting the speed: 120 km/h = (120 * 1000) m/3600 s = 33.33 m/s (approximately, rounded to two decimal places)
Now, let's assume the length of the train as 'L' meters.
The train enters the tunnel and emerges completely after 5 minutes, which is equivalent to 300 seconds.
During this time, the train covers the length of the tunnel (9.5 km) plus its own length (L). Therefore, the distance covered by the train is equal to the total distance traveled by the train and the length of the tunnel.
Distance covered = Length of tunnel + Length of train = 9.5 km + L
Now, we know that the distance covered is equal to the product of speed and time:
Distance covered = Speed * Time
Therefore, we can write:
9.5 km + L = 33.33 m/s * 300 s
Simplifying:
9.5 km + L = 9999 m
Subtracting 9.5 km from both sides:
L = 9999 m - 9.5 km L = 9999 m - 9500 m L = 499 m
Hence, the length of the train is approximately 499 meters.