Lovers Reunited: Calculating Time Apart

[Shane_K]

I have a question which reads as follows:
After a long time apart, a young couple in love are running towards each other in the hallways of an airport. They are 30.0m apart. The husband is accelerating from rest at a rate of 0.7m/s2 (2 is squared), and the wife was moving at 3.4m/s and maintains her speed. How much time passes before they are finally together?

I just need help gathering the info from the question.
What I have so far:
Husband
-v1=0m/s
-acceleration=0.7m/s2 (2 is squared)
-distance=30.0m
-time=?

Wife
-v1=3.4m/s
-distance=30.0m
-t=?

Thanks in advance:)

 

[Astronuc]

One may infer from the problem that the husband starts accelerating when his wife is 30 m from him. During the same period of time, each is traveling to some common point.

Let x be the distance traveled by the wife, and then knowing the velocity that the wife travels, 3.4 m/s, the distance as a function of time is simply x = 3.4 t (t in seconds).

In the same time, when they meet, the husband must have traveled 30-x.

 

[kyle8921]

I would approach this question by using the principles of kinematics, which is the study of motion and its causes. In order to calculate the time it takes for the couple to be reunited, we can use the equation d=vt + 1/2at^2, where d is the distance, v is the initial velocity, a is the acceleration, and t is the time.

For the husband, we know that his initial velocity is 0 m/s and his acceleration is 0.7 m/s^2. We also know that the distance between the couple is 30.0 m. Plugging these values into the equation, we get:

30.0m = (0m/s)t + 1/2(0.7m/s^2)t^2

Simplifying, we get 0.35t^2 = 30.0m. Solving for t, we get t = 10.95 seconds.

For the wife, we know that her initial velocity is 3.4 m/s and she maintains her speed. We also know that the distance between the couple is 30.0 m. Plugging these values into the equation, we get:

30.0m = (3.4m/s)t + 0.5(0)t^2

Simplifying, we get 3.4t = 30.0m. Solving for t, we get t = 8.82 seconds.

Since the wife reaches the husband first, we can conclude that it takes 8.82 seconds for the couple to be reunited. It is important to note that these calculations are based on ideal conditions and do not take into account any external factors such as air resistance or friction. Nevertheless, this calculation provides an estimate of the time it takes for the couple to be reunited based on the given information.