An automobile traveling 95 km/h overtakes a 1.00km long train travelling in the same direction on a track parallel to the road. if the train's speed is 75km/h, how long does it take the car to pass it and how far will the car have traveled in this time? what are the results if the car and train are traveling in opposite directions?
Answers
The car is traveling at 95 km/h, and the train is at 75 km/h.
Remember the train is 1 km long.
a)
With respect to the train the car is not moving as much as 75 km/h.
The car with respect to the train is moving as much as 95 - 75 = 20 km/h
Recall the train is 1 km long.
Time to cover the 1km long train = Distance / speed = 1 / 20 = (1/20) hour.
= (1/20)*60 minutes = 3 minutes.
So the car would pass the train in 3 minutes.
b)
Now if they are traveling in opposite directions;
the car with respect to the train = 75 + 95 = 170 km/h
Time to cover the 1km long train = Distance / speed = 1 / 170 = (1/170) hour.
= (1/170)*60 minutes = (6/17) minutes
= (6/17)*60 seconds = 360/17 seconds ≈ 21.176 seconds.
SameDirection: The car takes 3 minutes to pass the train and travels 4.75 km in this time.
Opposite Directions: The car takes about 0.35 minutes to pass the train and travels approximately 559 meters in this time.
SameDirection:
When the car overtakes the train, it has to cover the entire length of the train, which is 1.00 km.
Relative speed of the car with respect to the train = Car's speed - Train's speed
Relative speed = 95 km/h - 75 km/h
= 20 km/h
Now, we can calculate the time it takes for the car to overtake the train:
Time = Distance / Relative speed
Time = 1.00 km / 20 km/h
Time = 0.05 hours
=3 minutes(since 1 hour = 60 minutes, this is 0.05 x 60 = 3 minutes)
Hence, it takes the car 3 minutes to pass the train when they are traveling in the same direction.
Now, let's calculate how far the car has traveled in this time:
Distance traveled by the car = Car's speed x Time
Distance traveled by the car = 95 x 0.05
Distance traveled by the car = 4.75 km
So, when the car overtakes the train while traveling in the same direction, it takes 3 minutes, and the car will have traveled 4.75 km in that time.
Opposite Directions:
When the car and train are traveling in oppositedirections, they are moving towards each other.
In this case, the relative speed will be the sum of their speeds.
Relative speed of the car and train = Car's speed + Train's speed
Relative speed = 95 km/h + 75 km/h
= 170 km/h
To calculate the time it takes for the car to pass the train:
Time = Distance / Relative speed
Time = 1.00 km / 170 km/h
Time = 0.005882 hours (approximately 0.35 minutes)
So, it takes the car about 0.35 minutes to pass the train when they are traveling in opposite directions.
Now, let's calculate how far the car has traveled in this time:
Distance traveled by the car = Car's speed x Time
Distance traveled by the car = 95 km/h x 0.005882 hours
Distance traveled by the car = 0.5588 km (approximately 559 meters)
Hence, when the car and train are traveling in opposite directions, it takes about 0.35 minutes, and the car will have traveled approximately 559 meters in that time.
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