Two locomotives approach each other on parallel tracks. Each has a speed of v = 85 km/h with respect to the ground. If they are initially d = 7.0 km apart, how long will it be before they reach each other?
Since both vehicles are travelling at the same speed, they will meet at the midpoint.
d = V*t = 7km/2 = 3.5 km.
t = d/V = 3.5/85 = 0.04117647 h = 2.47 min.
To find out how long it will take for the two locomotives to reach each other, we can use the formula:
time = distance / relative speed
First, let's find the relative speed of the two locomotives. Since they are moving towards each other, we need to add up their individual speeds. In this case, both locomotives have a speed of v = 85 km/h.
Relative speed = 85 km/h + 85 km/h = 170 km/h
Now, let's calculate the time it will take for them to reach each other. We have the initial distance between them, which is d = 7.0 km.
time = 7.0 km / 170 km/h
To convert kilometers to miles, we can use the conversion factor 1 km = 0.621371 miles.
time = (7.0 km / 170 km/h) * (0.621371 miles/km)
Now, we can calculate the time:
time ≈ (7.0 * 0.621371) / 170 hours
time ≈ 0.0407165 hours
Since the answer is in hours, we can convert it to minutes. There are 60 minutes in an hour:
time ≈ 0.0407165 * 60 minutes
time ≈ 2.443 minutes
Therefore, it will take approximately 2.443 minutes for the two locomotives to reach each other.