How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 20.0 km/h when the cars' front bumpers are initially 75 m apart?
I just answered this duplicate posting
So the relative velocity is 40km/hr.
The relative distance is 75m
distance=velocity*time
.075km=40km/hr * time
time=.075/40 hrs. I get a little over six seconds.
To calculate the time it takes for the automobile in the left lane to overtake the car in the right lane, we need to determine how much time it takes for the distance between the two cars to reduce to zero.
Step 1: Convert the speeds from km/h to m/s:
- Speed of the automobile in the left lane (v1) = 60.0 km/h = (60.0 * 1000) / (60 * 60) = 16.67 m/s
- Speed of the car in the right lane (v2) = 20.0 km/h = (20.0 * 1000) / (60 * 60) = 5.56 m/s
Step 2: Calculate the relative velocity between the automobile and the car:
- Relative velocity (v_rel) = v1 - v2 = 16.67 m/s - 5.56 m/s = 11.11 m/s
Step 3: Calculate the time needed to cover the initial distance of 75 m:
- Time to cover the initial distance (t) = distance / relative velocity = 75 m / 11.11 m/s
Step 4: Calculate the time it takes for the automobile to overtake the car:
- Time to overtake (t_overtake) = 2 * t
By plugging in the values and performing the calculations, we can determine the final answer.
To find out how long it takes for the automobile in the left lane to overtake the car in the right lane, we can use the concept of relative velocity.
Step 1: Find the relative velocity between the two cars.
The relative velocity is the difference between the velocities of the two cars. In this case, the car in the left lane is traveling at 60.0 km/h (or 60,000 m/3600 s) and the car in the right lane is traveling at 20.0 km/h (or 20,000 m/3600 s). So the relative velocity is 60,000 m/3600 s - 20,000 m/3600 s = 40,000 m/3600 s.
Step 2: Use the relative velocity to calculate the time taken to overtake.
The distance between the cars' front bumpers is given as 75 m. To become even with the car in the right lane, the automobile in the left lane needs to cover this distance. The formula to calculate the time is:
Time = Distance / Speed
In this case, the distance is 75 m and the speed is the relative velocity we calculated earlier, which is 40,000 m/3600 s. Plugging in the values, we get:
Time = 75 m / (40,000 m/3600 s)
= 75 m * (3600 s/40,000 m)
= 6.75 s
Therefore, it takes approximately 6.75 seconds for the automobile in the left lane to overtake the car in the right lane and become even with it.