Concept explainers
The time taken by the car to pass the train and the distance travelled by the car in this time if the car and train are travelling in same direction. Also the time taken by the car to pass the train and the distance travelled by the car if the car and train are travelling in opposite directions.
Answer to Problem 73GP
The time taken by the car to pass the train if the car and train are travelling in same direction is
The distance traveled by the car in this time if the car and train are travelling in same direction is
The time taken by the car to pass the train if the car and train are travelling in opposite directions is
The distance traveled by the car in this time if the car and train are travelling in opposite directions is
Explanation of Solution
Given:
The speed of the car is
The length of the train is
The speed of the train is
Formula used:
The expression for relative speed is,
Here,
The expression for the time is,
Here, d is the distance travelled and v is the relative speed.
The expression for the distance travelled is,
Here,
Calculation:
Consider the car and train is travelling in same direction.
The relative speed is,
The time taken by the car to pass the train is,
The distance travelled by the car, if both are travelling in same direction, is
The relative speed , when both vehicles are travelling in opposite directions, is
The time taken by the car to pass the train, if both are travelling in opposite direction, is
The distance travelled by the car if the car and train is travelling in opposite direction is,
Conclusion:
Thus, the time taken by the car to pass the train if the car and train are travelling in same direction is
Thus, the distance travelled by the car in this time if the car and train are travelling in same direction is
Thus, the time taken by the car to pass the train if the car and train are travelling in opposite directions is
Thus, the distance traveled by the car in this time if the car and train are travelling in opposite directions is
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