A motorcycle traveling on the highway at a velocity of 120 km/h passes a car traveling at a velocity of 90 km/h in the same direction. From the point of view of a passenger in the... A motorcycle traveling on the highway at a velocity of 120 km/h passes a car traveling at a velocity of 90 km/h in the same direction. From the point of view of a passenger in the car, how much time will the car take to overtake the motorcycle in this case?
Understand the Problem
The question is asking how long it will take for a car, traveling slower than a motorcycle, to overtake that motorcycle from the perspective of a passenger in the car. This involves understanding relative velocity and time calculations based on the given speeds.
Answer
The time taken for the car to overtake the motorcycle is $\infty$ hours.
Answer for screen readers
The time taken for the car to overtake the motorcycle is $\infty$ hours.
Steps to Solve
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Identify the velocities The motorcycle is traveling at a velocity of 120 km/h, and the car is traveling at a velocity of 90 km/h.
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Calculate the relative velocity The relative velocity of the car with respect to the motorcycle is calculated as: $$ \text{Relative Velocity} = \text{Velocity of Car} - \text{Velocity of Motorcycle} $$ $$ \text{Relative Velocity} = 90 , \text{km/h} - 120 , \text{km/h} = -30 , \text{km/h} $$
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Understanding the relative motion A negative relative velocity indicates that the car is slower than the motorcycle. From the car's perspective, the motorcycle is moving away.
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Determining the time to overtake Since the car is slower, it will never overtake the motorcycle. Thus, the time taken to overtake is: $$ \text{Time} = \frac{\text{Distance}}{\text{Relative Velocity}} $$ However, since the distance required to overtake is effectively infinity (as the motorcycle moves away), the time can be understood as: $$ \text{Time} = \infty $$
The time taken for the car to overtake the motorcycle is $\infty$ hours.
More Information
This scenario illustrates the concept of relative velocity. When one object moves faster than another in the same direction, the slower object can never catch up.
Tips
- Assuming the car will eventually overtake the motorcycle without considering the relative speeds.
- Miscalculating relative velocity by mixing up addition and subtraction.
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