a train of length 100m runs at a speed of 120km/hr from north to south. another train of length 150m travels with a speed of 80 km/hr from south to north. what is the time required to cross each other ?
Total length = 100+150= 250m
Total speed =120+80 = 200km/hr= 200*5/18 m/s
Time = 250/(200*5/18) = (250*18)/(200*5) = 4500/1000 = 4.5s
To find the time required for the two trains to cross each other, we can use the relative speed of the trains.
Step 1: Convert the speeds from km/hr to m/s.
- The speed of the first train is 120 km/hr = (120 * 1000) m/3600 s = 33.33 m/s.
- The speed of the second train is 80 km/hr = (80 * 1000) m/3600 s = 22.22 m/s.
Step 2: Calculate the relative speed.
- When two objects are moving towards each other, their relative speed is the sum of their individual speeds.
- The relative speed of the trains = 33.33 m/s + 22.22 m/s = 55.55 m/s.
Step 3: Calculate the total distance to be covered when the two trains cross each other.
- The length of the first train is given as 100m.
- The length of the second train is given as 150m.
- The total distance to be covered is the sum of the lengths of both trains: 100m + 150m = 250m.
Step 4: Calculate the time required.
- Time = Distance / Speed
- Time = 250m / 55.55 m/s ≈ 4.5 seconds.
Therefore, it takes approximately 4.5 seconds for the two trains to cross each other.
To determine the time required for the two trains to cross each other, we need to find the point at which their paths intersect. In other words, we need to determine the distance they need to cover to reach that point.
Let's calculate the distance for the train moving from north to south:
The length of the first train is 100m (given).
Since the train is moving from north to south, the distance it needs to cover relative to the stationary observer is equivalent to the length of the train, which is 100m.
For the train moving from south to north:
The length of the second train is 150m (given).
Again, the distance it needs to cover relative to the stationary observer is equal to the length of the train, which is 150m.
Now, let's calculate the combined distance they need to cover to cross each other:
The distance required is the sum of the lengths of the two trains, which is 100m + 150m = 250m.
Next, let's convert the speed of the first train into meters per second:
Speed = 120 km/hr = (120,000m / 3600s) m/s = 33.33 m/s (approximately)
Similarly, let's convert the speed of the second train into meters per second:
Speed = 80 km/hr = (80,000m / 3600s) m/s = 22.22 m/s (approximately)
Now that we know the distance the two trains need to cover and their respective speeds, we can calculate the time required for them to cross each other using the formula:
Time = Distance / Relative Speed
Relative Speed = Speed of the first train + Speed of the second train
Plugging in the values, we get:
Relative Speed = 33.33 m/s + 22.22 m/s = 55.55 m/s
Time = 250m / 55.55 m/s ≈ 4.5 seconds
Therefore, it would take approximately 4.5 seconds for the two trains to cross each other.
Let the faster train be train A.
Let the slower train be train B.
The speed of train A relative to train B, and vice- versa, is 120 km/h + 80 km/h =200 km/h.
The distance traversed from when the fronts of the trains meet each other (presumably on separate tracks!) and the backs of the trains depart from each other is the sum of the trains' lengths = 100 m + 150 m = 250 m = 0.25 km
t = d/v
t = 0.25 km / 200 km/h
t = ____