a train 100 m long is to cross a river of a bridge of length 800 m what time will it take to cross the bridge the train moves with a velocity of 36 km h
find the velocity in m/s ... 36 km/h ---> ? m/s
crossing starts when the front of the train enters the bridge
... it finishes when the end of the train leaves the bridge
how far does the "whole" train have to move?
To find the time it takes for the train to cross the bridge, we need to consider two components: the time it takes for the train to cross the river and the time it takes for the train to cross the bridge.
First, let's calculate the time it takes for the train to cross the river. Since the train is moving perpendicular to the river, we can treat the movement as a right triangle. The hypotenuse of the right triangle is the diagonal path of the train across the river, and the train's length forms one side of the triangle.
Using Pythagoras' theorem, we can find the length of the diagonal path across the river:
(diagonal path)^2 = (train's length)^2 + (bridge length)^2
(diagonal path)^2 = (100m)^2 + (800m)^2
(diagonal path)^2 = 10000m^2 + 640000m^2
(diagonal path)^2 = 650000m^2
Taking the square root of both sides, we find:
diagonal path = √650000m
diagonal path ≈ 806.225m
The train's velocity is given in km/h, so it needs to be converted to m/s for further calculations. There are 1000m in 1 km, and 1 hour is 3600 seconds. Thus, the conversion factor is 1000/3600 = 5/18.
Converting the train's velocity:
Velocity = 36 km/h × (5/18) m/s
Velocity ≈ 10 m/s
Now, let's calculate the time it takes for the train to cross the river:
Time = Distance/Velocity
Time = 806.225m / 10m/s
Time ≈ 80.62s
Next, we calculate the time it takes for the train to cross the bridge:
Time = Distance/Velocity
Time = 800m / 10m/s
Time = 80s
Finally, to find the total time it takes for the train to cross the bridge, we add the time it takes to cross the river and the time it takes to cross the bridge:
Total Time = Time to cross river + Time to cross bridge
Total Time ≈ 80.62s + 80s
Total Time ≈ 160.62s
Therefore, it will take approximately 160.62 seconds for the train to cross the 800m long bridge.