A train , 100 m long, is running at a speed of 54 km/hr. If it crosses a bridge in 12 seconds, find the length of the bridge.
If the bridge's length is x, then the train's engine has to move (x+100) meters to pull the last car across. So, since distance = speed * time,
x+100 = 54000 * 12/3600
change km/hr to m/s
find how long for the train to pass a given point ... t
length of bridge = (12 - t) * speed of train
To find the length of the bridge, we need to calculate the time it takes for the train to cross the bridge.
Given:
Length of the train = 100 m
Speed of the train = 54 km/hr
First, let's convert the speed from km/hr to m/s. We know that 1 km/hr is equal to 1000 m/3600 s (3600 seconds in an hour).
So, the speed of the train in m/s is (54 km/hr) × (1000 m/3600 s) = 15 m/s.
Now, let's calculate the time it takes for the train to cross the bridge.
We can use the formula: Time = Distance / Speed
Since the total distance traveled by the train to cross both the train length and the bridge length, we can write:
Time = (Length of train + Length of bridge) / Speed
Given:
Time = 12 seconds
Length of train = 100 m
Speed = 15 m/s (calculated earlier)
Plugging in the values, we get:
12 = (100 + Length of bridge) / 15
To isolate the Length of the bridge, we can cross multiply and then solve the equation:
12 × 15 = 100 + Length of bridge
180 = 100 + Length of bridge
Now, we can solve for the Length of the bridge by subtracting 100 from both sides:
180 - 100 = Length of bridge
Length of bridge = 80 meters
Therefore, the length of the bridge is 80 meters.