# How to calculate distance required for observable difference

• Dain Ironfoot
In summary, Me and my grandfather had a debate on whether objects fall at the same rate on Earth independent of air resistance or not. He believes that all objects fall at the same rate, while I argue that air resistance affects the speed at which objects fall. We both lack knowledge in physics, so I asked for help. I suggested dropping a leaf and a rock, but my grandfather claimed the feather has no mass. I remembered that as a kid, I used to drop a toy paratrooper and a rock to see the difference in speed. I found calculators to determine the difference, but I don't understand the math. I suggested reading a wiki article, but it only calculates for simple objects. I asked my grandfather why parachut
Dain Ironfoot
Me and my grandfather got into a "debate" (more like one-sided argument) on whether objects fall at the same rate on Earth independent of air resistance or not. He claims that "If you drop 2 objects from an airplane -- like a car and a marble, both objects would hit the ground at the same time.", I say no, because the car has a larger surface area and the marble would hit first due to less air resistance (Neither of us really know anything about physics [that's why I'm here]).

I've sent him tons of links on the subject but he's still determined he's right because "that's the way he was taught in school". There's not many high places here for me to drop 2 objects off of to see the results, so my question is:

How high must we be to be able to observe a noticeable difference in when the two objects hit the ground? How do I calculate the approximate difference of objects hitting the ground? For simplicity let's say the 2 objects I am dropping are: a 2kg 1m square, and a 2kg 1m diameter sphere.

As a kid I had a toy paratrooper with a plastic parachute that I would fling into the air and wait for him to parachute down. I was able to tell the difference pretty easily between my paratrooper and a rock.

So you don't really need to even get into the math. Just have your grandfather go throw a leaf and a rock in the air and see which one hits the ground first.

Try to explain to your father what is the "school science".

Dain Ironfoot
Drakkith said:
Just have your grandfather go throw a leaf and a rock in the air and see which one hits the ground first.

Something similar was literally one of the first things I tried, I suggested dropping a rock and a feather but he claims a feather has no mass. Regardless, this is something I find interesting and would like to know. I've found calculators that could calculate it for me but I don't understand how it arrives at the conclusion.

Drakkith said:
As a kid I had a toy paratrooper with a plastic parachute that I would fling into the air and wait for him to parachute down. I was able to tell the difference pretty easily between my paratrooper and a rock.
That's it. That's how I'm going to prove it to him, I used to do the same thing but that was so long ago I forgot!

Dain Ironfoot said:
Something similar was literally one of the first things I tried, I suggested dropping a rock and a feather but he claims a feather has no mass.

Ask him if a paratrooper also has no mass!

Dain Ironfoot said:
Regardless, this is something I find interesting and would like to know. I've found calculators that could calculate it for me but I don't understand how it arrives at the conclusion.

Not sure how much I can help you, as I don't fully understand all the details myself. Give this wiki article a read and see if it helps: http://en.wikipedia.org/wiki/Terminal_velocity
The 'Physics' section contains the math needed to find the terminal velocity of the object based on its mass, drag coefficient (highly dependent on shape), and projected area (the part of the object facing into the wind). Note that for a real, non-simple object (i.e. not a simple cube, sphere, cone, or other basic shape) finding the terminal velocity is much more complicated, since its drag coefficient isn't easily found. Still, you should be able to get to some reasonable approximation with it.

Dain Ironfoot
Ask your grandfather why parachutists bother to pull their rip cords if air resistance doesn't slow them down.

davenn and Dain Ironfoot

## 1. What is the formula for calculating distance required for observable difference?

The formula for calculating distance required for observable difference is D = (2 x R) x tan(A/2), where D is the distance, R is the distance between the two objects, and A is the angle of observation.

## 2. Can the distance required for observable difference be calculated for any two objects?

Yes, the formula for calculating distance required for observable difference can be used for any two objects as long as the distance between them and the angle of observation are known.

## 3. How accurate is the calculated distance for observable difference?

The accuracy of the calculated distance for observable difference depends on the accuracy of the measured distance and angle of observation. The smaller the measurement errors, the more accurate the calculated distance will be.

## 4. Is there a limit to the distance required for observable difference?

Yes, there is a limit to the distance required for observable difference. This limit is determined by the resolving power of the observer's eyes or the resolution of the measuring instrument being used.

## 5. Are there any other factors that can affect the distance required for observable difference?

Yes, there are other factors that can affect the distance required for observable difference, such as atmospheric conditions, lighting, and the size and contrast of the objects being observed.

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