# An average velocity question

geepamoogle
Posers and Puzzles 21 Feb '07 21:27
1. 21 Feb '07 21:27
A fairly simple math poser.

I plan on making a two-way car trip to a particular location, and I wish to average 50 mph for the entire trip. However, on my way up there, I get slowed by some trouble on the road, and only average 25 mph on the way up there. How fast do I have to go on the way back in order to average 50 mph?
2. 21 Feb '07 21:31
Originally posted by geepamoogle
A fairly simple math poser.

I plan on making a two-way car trip to a particular location, and I wish to average 50 mph for the entire trip. However, on my way up there, I get slowed by some trouble on the road, and only average 25 mph on the way up there. How fast do I have to go on the way back in order to average 50 mph?
FTL?
3. sonhouse
Fast and Curious
21 Feb '07 21:33
Originally posted by geepamoogle
A fairly simple math poser.

I plan on making a two-way car trip to a particular location, and I wish to average 50 mph for the entire trip. However, on my way up there, I get slowed by some trouble on the road, and only average 25 mph on the way up there. How fast do I have to go on the way back in order to average 50 mph?
I already posted this kind of problem, the answer is you can't, you have to have infinite velocity going back, say the trip is 100 miles, 4 hours at 25 MPH, so if you take zero time coming back, you do 200 Miles in 4 hours or 50 mph, so you can't. Even at the speed of light you would only get close to 50 mph, not exactly. Speed of light is about 5.3 microseconds per mile so even a light beam would take
530 microseconds to go back, that would put you at 49.99999 something mph average.
4. 21 Feb '07 21:35
I figured that one would be too easy. ๐ And I missed your post of this nature. Relatively new here.
5. sonhouse
Fast and Curious
21 Feb '07 21:44
Originally posted by geepamoogle
I figured that one would be too easy. ๐ And I missed your post of this nature. Relatively new here.
Don't do helium balloon problem's either, I did them to death, much to the chagrin of the puzzle poster crowd๐
6. 21 Feb '07 21:531 edit
Originally posted by sonhouse
... Even at the speed of light you would only get close to 50 mph, not exactly. Speed of light is about 5.3 microseconds per mile so even a light beam would take
530 microseconds to go back, that would put you at 49.99999 something mph average.
This was the very reason that I stated 'Faster Than Light'.
Lights velocity is simply not enough.
Perhaps we have to invoke some quantum mechanics into the equations...?
Or spacial worm holes or something. Magic might suffice.
7. 21 Feb '07 22:01
sonhouse is right. I would have to make the return trip instantaneously, and thusly travel at inifinite speed.

I can't recall a/the helium poser, so it's safe. There was another I had thought of, but I forget which one it is..

I do remember a weighing one I came up with though. (Most every other one I've heard and passed along, rather than crafting it myself.)
8. sonhouse
Fast and Curious
21 Feb '07 22:07
Originally posted by geepamoogle
sonhouse is right. I would have to make the return trip instantaneously, and thusly travel at inifinite speed.

I can't recall a/the helium poser, so it's safe. There was another I had thought of, but I forget which one it is..

I do remember a weighing one I came up with though. (Most every other one I've heard and passed along, rather than crafting it myself.)
The first of my helium balloon puzzles: You are in a large cylindrical spacecraft with an engine at one end, say behind you. the inside of the cylinder is filled with normal breathable air. In the center of the cylinder you carefully place a helium filled balloon and there are no air currents so it stays put when you back off. Then you fire a rocket engine, the one behind you. What happens to the helium balloon?
9. 21 Feb '07 22:14
Originally posted by sonhouse
The first of my helium balloon puzzles: You are in a large cylindrical spacecraft with an engine at one end, say behind you. the inside of the cylinder is filled with normal breathable air. In the center of the cylinder you carefully place a helium filled balloon and there are no air currents so it stays put when you back off. Then you fire a rocket engine, the one behind you. What happens to the helium balloon?
Interesting problem. I think I know the answer.

But...

Let's say that you travel with this particular spacecraft with a velocity very near the velocity of light. Then you move the balloon with your hand so much aft as you can. Then you suddenly accelerate the ship to a velocity 50% (or so) nearer to the velocity of light. The balloon will move of course but will it move faster than light toward the front of the ship?
10. 21 Feb '07 22:19
Aaah, physics.. Been a while since I've had to answer one like that.

I may be confusing with another (similar) poser, but my guess would be that in a weightless environment like space, you would be dealing with a closed system, and the system would move as one, which suggests the balloon would remain in its position relative to the ship.

However, the althernative argument would be that initially the balloon would remain where it is while the ship moves forwards, but that the air in the container would begin to be pushed and push forward, resulting in the balloon shifting for a brief moment before stabilizing.

A third alternative would be that the second case would result in some currents, owing to the air's greater fluidity, in which case an airflow would be setup which might cause some interesting and chaotic motion of the balloon.

As you can see, I don't have the answer, and thus cannot pose the problem with any authority.

The poser I MAY be confusing this with involves a moving truck with some birds in the back. If the birds become airborne within the back, does the truck get lighter (as weighed by a weighing machine)?
11. sonhouse
Fast and Curious
21 Feb '07 22:251 edit
Originally posted by geepamoogle
Aaah, physics.. Been a while since I've had to answer one like that.

I may be confusing with another (similar) poser, but my guess would be that in a weightless environment like space, you would be dealing with a closed system, and the system would move as one, which suggests the balloon would remain in its position relative to the ship.

However come airborne within the back, does the truck get lighter (as weighed by a weighing machine)?
The answer to the bird question is it would be exactly the same weight because in order for the birds to be suspended, they have to impart thrust and that thrust comes from moving the air and that air is confined to the back of the truck so all the forces even out and they weigh the same if they are on their perches or flying. In order to answer the balloon problem correctly, think about what would happen to the balloon if the spacecraft was simply sitting straight up on the earth, think of the Washington monument. You are in the center and let go the balloon. You have to remember Einstein's 'equivalence of gravity and acceleration'. NOW think about the balloon inside the rocket somewhere in space, without the engine running and with the rocket running.
12. 21 Feb '07 22:59
The obvious answer would be it would be pressed against the back, but with physics questions, the obvious answer is sometimes wrong. For instance, a helium balloon's lesser density than breathable air might have an effect.

My question would be how the internals of the closed system interact, as this would determine how the force of the rocket gets distributed throughout the components and hence what happens with any single component relative to the others.

For instance, suppose this rocket's center was composed of a light but solid crystalline structure. In this case, there is no doubt that it would behave as one, rather than as distinct components, and were there to be a helium balloon in the middle, it would remain in the middle.

If the core wore a highly viscous liquid, then it may behave differently.

This has the potential of getting into the higly chaotic area of fluid mechanics. However, that's probably making it too complicated.
13. sonhouse
Fast and Curious
22 Feb '07 13:44
Originally posted by geepamoogle
The obvious answer would be it would be pressed against the back, but with physics questions, the obvious answer is sometimes wrong. For instance, a helium balloon's lesser density than breathable air might have an effect.

My question would be how the internals of the closed system interact, as this would determine how the force of the rocket gets di ...[text shortened]... e higly chaotic area of fluid mechanics. However, that's probably making it too complicated.
Way too complicated, re-read my last post or read it if you missed it.
Put that same rocket down on the ground, upright with the rocket at the bottom end. What happens to the balloon now? I am trying to get you to think about the equivalence of acelleration and gravity here.
14. 22 Feb '07 14:46
When the craft is upright on the ground, the helium balloon goes to the top. In space, when the rocket is fired it moves to the front.
15. sonhouse
Fast and Curious
22 Feb '07 15:14
Originally posted by luskin
When the craft is upright on the ground, the helium balloon goes to the top. In space, when the rocket is fired it moves to the front.
Give the man a prize! You got it. I mentioned the equivalence law and tried to get that across, don't quite understand why that is so difficult for people to understand. When I posted this problem a year ago, I had to throw in so many hints like, Ok, now imagine that balloon is right next to a bowling ball, what happens to them? Hint hint๐
People need to learn visualization I guess.