How long does it take an automobile traveling in the left lane at 120.0 km/h to overtake (become even with) another car that is travelling in the right lane at 100.0 km/h, when the car’s front bumpers are initially 200.0 m apart?
To find out how long it takes for the left-lane car to overtake the right-lane car, we need to determine the time it takes for the distance between the two cars to decrease from 200.0 m to 0.
Let's convert the speeds of the cars into meters per second:
Speed of the left-lane car = 120.0 km/h = (120.0 * 1000) / 3600 = 33.33 m/s
Speed of the right-lane car = 100.0 km/h = (100.0 * 1000) / 3600 = 27.78 m/s
Now, we can calculate the relative speed of the left-lane car with respect to the right-lane car:
Relative speed = Speed of the left-lane car - Speed of the right-lane car
= 33.33 m/s - 27.78 m/s
= 5.55 m/s
Now, let's calculate the time it takes for the left-lane car to travel a distance of 200.0 m with a speed of 5.55 m/s:
Time = Distance / Speed
= 200.0 m / 5.55 m/s
≈ 36.04 seconds
Therefore, it will take approximately 36.04 seconds for the left-lane car to overtake the right-lane car.