Two locomotives approach each other on parallel tracks. Each has a speed of v = 95 km/h with respect to the ground. If they are initially d = 7.5 km apart, how long will it be before they reach each other?
The speed at which the two objects are approaching each other (from the trains' perspective) is 95 km/h (x 2) = 190 km/h.
If they are 7.5 km apart at first, you can set up a proportion:
190 km 7.5 km
------ = ---------
1 hr x hr
Cross-multiply the terms and set them equal to each other.
(190 km)(x hr) = (7.5 km)(1 hr)
Divide both sides by (190 km).
(190 km)(x hr) = (7.5 km)(1 hr)
-------------- --------------
190 km 190 km
x hr = (7.5 kmh)/190 km
x hr = 0.03947368421 hr.
(sig figs = 0.039 hr)
The unit of hr. may not be very useful in this case, so let's convert hrs to min using dimensional analysis:
0.03947368 hr 60 min
------------- x ------------
1 1 hr
= 2.36 minutes
(sig figs = 2.4 minutes)
Hope this helps!
To find the time it takes for the two locomotives to reach each other, we need to use the equation of motion: distance = speed × time.
Let's assume that the position of one locomotive is fixed, and the other locomotive is approaching it. Since both locomotives are moving towards each other, their effective speed, relative to each other, is the sum of their speeds. In this case, it would be 95 km/h + 95 km/h = 190 km/h.
The total distance they need to cover is the initial distance between them, which is 7.5 km.
Now, we can rearrange the equation distance = speed × time to solve for time: time = distance / speed.
Plugging in the values we have:
time = 7.5 km / 190 km/h.
Before dividing, let's ensure that the units are consistent. We convert the distance in kilometers to meters to match the speed in meters per hour:
time = (7.5 km * 1000 m/km) / (190 km/h * 1000 m/km).
Simplifying, we get:
time = 7500 m / 190000 m/h.
Dividing, we find:
time = 0.03947 hours.
To express this time in minutes, we can multiply by 60 since there are 60 minutes in an hour:
time = 0.03947 hours * 60 minutes/hour.
Calculating, we get:
time ≈ 2.37 minutes.
Therefore, it will take approximately 2.37 minutes for the two locomotives to reach each other.
To calculate how long it will be before the two locomotives reach each other, we can use the formula:
time = distance / relative speed
First, we need to find the relative speed of the two locomotives. Since they are moving towards each other, we need to add their speeds together:
relative speed = 95 km/h + 95 km/h
relative speed = 190 km/h
Next, we can calculate the time it takes for them to reach each other by dividing the initial distance by the relative speed:
time = 7.5 km / 190 km/h
time = 0.03947 hours
Since the answer is in hours, we can convert it to minutes by multiplying by 60:
time = 0.03947 hours * 60 minutes/hour
time ≈ 2.368 minutes
Therefore, it will take approximately 2.368 minutes for the two locomotives to reach each other.