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#61 mrbojangles

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Posted 13 July 2007 - 04:28 PM

This is not as elegant a solution, but...

If you were on a planet with just the right mass and diameter, you're hardest throw in the right direction would allow the ball to orbit the planet once (or twice, etc. depending on the constants just mentioned).



here's why that's a problem. the earth's diameter is about 7900 miles. when the ball is thrown it will not only be traveling around the world but also falling. what that means is that the ball has to travel 7900 miles before it falls 6 feet. with some physics (or a stop watch) we find that an object falls to the earth from 6 feet in about 0.61 seconds. convert 7900 miles per 0.61 seconds to mph and you get 46,622,951 mph!! earth's escape velocity is 25000 mph. so once you threw the ball at 47,000,000 mph it would just keep going out into space instead of curving around the earth.
sorry
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#62 mrbojangles

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Posted 13 July 2007 - 04:30 PM


This is not as elegant a solution, but...

If you were on a planet with just the right mass and diameter, you're hardest throw in the right direction would allow the ball to orbit the planet once (or twice, etc. depending on the constants just mentioned).



here's why that's a problem. the earth's diameter is about 7900 miles. when the ball is thrown it will not only be traveling around the world but also falling. what that means is that the ball has to travel 7900 miles before it falls 6 feet. with some physics (or a stop watch) we find that an object falls to the earth from 6 feet in about 0.61 seconds. convert 7900 miles per 0.61 seconds to mph and you get 46,622,951 mph!! earth's escape velocity is 25000 mph. so once you threw the ball at 47,000,000 mph it would just keep going out into space instead of curving around the earth.
sorry


ok, i realize you said if you were on the right planet with just the right mass and diameter and you're right about that (i kind of want to calculate this one for the moon now) but i wanted to at least show people why that solution wouldn't work here on our home planet
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#63 mrbojangles

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Posted 13 July 2007 - 04:43 PM


This is not as elegant a solution, but...

If you were on a planet with just the right mass and diameter, you're hardest throw in the right direction would allow the ball to orbit the planet once (or twice, etc. depending on the constants just mentioned).



here's why that's a problem. the earth's diameter is about 7900 miles. when the ball is thrown it will not only be traveling around the world but also falling. what that means is that the ball has to travel 7900 miles before it falls 6 feet. with some physics (or a stop watch) we find that an object falls to the earth from 6 feet in about 0.61 seconds. convert 7900 miles per 0.61 seconds to mph and you get 46,622,951 mph!! earth's escape velocity is 25000 mph. so once you threw the ball at 47,000,000 mph it would just keep going out into space instead of curving around the earth.
sorry



AAARRRGGGHHHH!!!! I just realized I used the diameter when I should have been looking at the circumference. Here it is again, revised
earth's diameter: 24900 miles
drop height: 6 ft
drop time: 0.61 seconds
necessary object speed: 146,950,819.7 mph
ha! you'd have to throw it pi times faster than i erroneously calculated. good luck with that
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#64 mrbojangles

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Posted 13 July 2007 - 05:15 PM

and as a final FYI.
On the moon.
escape velocity: 5300 mph
gravity: 5.33 ft/s^2
drop time: 1.061 seconds
necessary object speed: 23,038,821 mph

Given all earth conditions are the same except for the earth's circumference
the circumference would have to be: no more than 4.2 miles
the object's thrown speed would have to be: 24767.89 mph
which would mean it's density would be: as best as i can calculate-about 10^1013 lb/ft^3
which means that earth would basically be close to a black hole. and, of course, if the density were this great then the gravity would change and you'd have to recalculate it again.

another interesting way to look at it that i just thought of is to compare the object speeds to the speed of light. taking earth as it is, i found earlier that the ball would have to be thrown at about 147,000,000 mph
speed of light: 670,600,000 mph
so about 1/5 the speed of light
again, good luck with that
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#65 mathemagister

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Posted 14 July 2007 - 10:39 AM

Einsteins theorised (and later proved) effects would start to be noticable on the ball. In the observer's frame of reference: the ball would look squished horizontally (the direction it was moving), its mass would increase and less time would appear to pass on it.
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#66 hafiz169

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Posted 14 July 2007 - 06:26 PM

you would throw the ball streight above your head and then it will come back to you.
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#67 wrzesinski

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Posted 15 July 2007 - 12:24 AM

ok, yall are making this problem way too complicated...just throw the ball up...straight up...gravity will take effect and the ball will fall back down to you...
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#68 unreality

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Posted 15 July 2007 - 12:27 AM

yeah, people. this is supposed to be a simple riddle with a catch. there should be no more discussion after we know the catch. jeez.
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#69 ReikoNanba

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Posted 19 July 2007 - 08:10 PM

You throw it upwards. what comes up will come down
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#70 ecoolhandluke

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Posted 19 July 2007 - 10:24 PM

throw it straight up, drrr
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