Two Balls Drop, what happens to the distance?

[Amad27]

Homework Statement

Ball A is dropped from the top of a building. One second later, ball B is dropped from the same building. As time progresses, the distance between them
A) increases. [<-- Correct Answer]
B) remains constant.
C) decreases.
D) cannot be determined from the information given.

Homework Equations

N/A

The Attempt at a Solution

[/B]
Keep in mind that the solution key could and is often wrong.

I would say it is D) Cannot be determined from the information given

Because we do not know the surface area of each of the Balls, Ball A & Ball B, thus we cannot determine air resistance, which affects the balls.

We do not know the initial velocity. It just says the ball is dropped from the top of a building. This does not provide the information about the velocity, which is critical in that.

$F_D = 0.5pv^2(C_D)(A)$ where this is the drag equation. http://en.wikipedia.org/wiki/Drag_equation

So we do not know the density of the fluid (air), we do not know the speed of the object either. Thus, we can't determine air resistance, which is important in the problem.

What other reasons can you possibly think of that could prove the answer is (D)?

Thanks!

 

[Orodruin]

I would believe that the problem constructor assumes that you can ignore air drag and that terminal velocity is therefore never reached or even approached by either ball. In this case the answer is unambiguously A. Can you argue for why this is so?

Edit: Also, "dropped" is typically taken to mean "with no initial velocity". Otherwise it is usually called "thrown".

 

[Simon Bridge]

In addition, the word "dropped" would indicate the balls start at rest ... otherwise the problem would say the balls were "thrown".

 

[Amad27]

I would believe that the problem constructor assumes that you can ignore air drag and that terminal velocity is therefore never reached or even approached by either ball. In this case the answer is unambiguously A. Can you argue for why this is so?

Edit: Also, "dropped" is typically taken to mean "with no initial velocity". Otherwise it is usually called "thrown".

Hello @Oroduin, and @Simon Bridge

That is my point; the problem constructor literally gave you all information.

If he/she did not give terminal velocity, or did not say neglect air drag, then we don't have to do that.

Which would mean there is not enough information given by the author right?

 

[Orodruin]

Well, I would say this depends on the intended audience. For example, in a high-school setting, you would typically not cover anything about drag and students would be expected to neglect it essentially because they have not been told about how to handle it. Even if you do include air drag, there could be an implicit assumption that the balls are identical, which would lead to the same conclusion. This could simply be laziness on the part of the author and, as I mentioned, depend on the intended audience.

 

[PeroK]

If they are table tennis balls and there's a strong, blustery wind blowing, as there often is round a tall building, then anything could happen!

 

[Amad27]

Well, I would say this depends on the intended audience. For example, in a high-school setting, you would typically not cover anything about drag and students would be expected to neglect it essentially because they have not been told about how to handle it. Even if you do include air drag, there could be an implicit assumption that the balls are identical, which would lead to the same conclusion. This could simply be laziness on the part of the author and, as I mentioned, depend on the intended audience.

Hello @Orodruin, the winds aren't mentioned either, and as @PeroK points out they could be table-tennis balls.

So basically what you are saying is that the accepted convention is that we simply don't assume what isn't mentioned doesn't exist right? That could perhaps be why the answer is A?

 

[Orodruin]

As I said earlier, it would depend a lot on the intended audience. Your thinking is correct and you have a level of reasoning which may be higher than that of the intended target group. If asked this question in a class of fluid dynamics, it is clear that there would not be enough information due to all the unknowns regarding the balls, winds, etc. However, if posed at a high-school level to a class which has never seen a problem with damping, it may be a reasonable assumption that the class is always working in the approximation where damping effects are ignored.

 

[CWatters]

The problem is that assumes all the students are taking the same courses. What happens when a few are taking extra courses that do cover problems involving damping.

When I was at school some 35+ years ago the Applied Maths and Physics courses treated the coefficient of friction and friction forces differently. You had to remember that on the Applied Maths course friction force was dependant on the contact area, whereas in Physics it wasn't.

 

[Orodruin]

The problem is that assumes all the students are taking the same courses. What happens when a few are taking extra courses that do cover problems involving damping.

When I was at school some 35+ years ago the Applied Maths and Physics courses treated the coefficient of friction and friction forces differently. You had to remember that on the Applied Maths course friction force was dependant on the contact area, whereas in Physics it wasn't.

I would say this is a general problem if you simply ask students to provide an answer without reasoning. In those cases you have to be very careful with how the question is phrased. As long as a student can give a reasonable physical argument for his/her response, I would consider it a valid solution (in qualitative questions, of course deductions could be made for mistakes in maths etc for more quantitative or algebraic questions).