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Free falling objects at different times.

1. Homework Statement
Alright so I was given the question " If two of the same object were dropped from the same height at different times, what would happen to the distance between the objects."


2. Homework Equations



3. The Attempt at a Solution I have thought about this for about a half an hour and even tried to do an experiment for this with no luck (I don't have a far enough drop to see if the distance between the two changes) I am debating both sides and can't seem to come to a conclusion.
 
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Are you supposed to take air resistance into account?
 
Air resistance is never brought up in the question.
 
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Hmm. In what context is the question set then? What had been studied just before?
 
We have simply been going through the basics of motion. When given a problem we have to extract final velocity, initial velocity,acceleration, position and time. Using the different equations we then find the missing variables. Resistance has not been added in just yet, all this is asking is if a ball was dropped a few seconds before another, would the first ball be moving away from the second ball. My original thought is that they would stay the same distance apart as they fell because the both started from rest, and both have the same acceleration, but I was then thinking that the longer an object is in the air the faster it is going, (up until terminal velocity) so would that mean the the distance between the two objects would get bigger, smaller or stay the same.
 
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You are thinking correctly that an object that has been accelerating longer, will always have a greater velocity that the other object. What does that mean with regard to the distance between the objects?
 
Okay what my professor is saying is if the first ball leaves my hand a second before the second ball will the distance between the two balls at free fall stay the same or will the first ball accelerate exponentially and move farther and farther away from the first one. The only axis involved is the Y axis, this is simply vertical distance from one another.
 
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Re-read #6 and answer the question.
 

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