Problem Statement:

A train 100m long is moving with a velocity of 60km/h. Find the time it takes to cross a bridge of 1km.

Solution:

To find the time it takes for the train to cross the bridge, we need to determine the relative velocity between the train and the bridge. Since the train is moving with a velocity of 60km/h, we need to convert this velocity to m/s.

Conversion of Velocity:
- Given: Velocity of train = 60 km/h
- Conversion: 1 km/h = 1000 m/3600 s
- Calculation: Velocity of train = (60 km/h) * (1000 m/3600 s)
= (60 * 1000) / 3600
= 60000 / 3600
≈ 16.67 m/s

Length of Train:
The length of the train is given as 100m.

Length of Bridge:
The length of the bridge is given as 1km, which is equal to 1000m.

Calculation of Relative Velocity:
The relative velocity between the train and the bridge is the difference between the velocity of the train and the velocity of the bridge.

- Calculation: Relative velocity = Velocity of train - Velocity of bridge
= 16.67 m/s - 0 m/s (since the bridge is stationary)
= 16.67 m/s

Time to cross the bridge:
To find the time it takes for the train to cross the bridge, we divide the length of the train by the relative velocity.

- Calculation: Time = Length of train / Relative velocity
= 100m / 16.67 m/s
≈ 6 seconds

Therefore, it takes approximately 6 seconds for the train to cross the bridge.

Conclusion:

In conclusion, to find the time it takes for a train to cross a bridge, we need to calculate the relative velocity between the train and the bridge. By dividing the length of the train by the relative velocity, we can determine the time taken. In this case, with a train length of 100m and a relative velocity of 16.67 m/s, it takes approximately 6 seconds for the train to cross a bridge of 1km.

Train length = 100 m
bridge length = 1 km = 1000 m
total = 1100 m
speed = 60 km \ hr
50/3 meter per sec

so time needed
= [1100/ 3 ] x 50
= 66 sec