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Old 22nd September 2007, 03:32 AM   #1
star882 is offline star882  United States
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Default Physics puzzle

There is a circular running track 168 feet in diameter. Peggy Liska runs 10 laps around the track in 6 minutes. What is her average velocity in meters per second?

Hint: Circumference is equal to diameter times pi. One meter is about 3.28 feet. One minute is 60 seconds.
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Old 22nd September 2007, 05:51 AM   #2
Nanook is offline Nanook  Canada
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Default zero...

velocity is a vector and as such follows rules of vector addition. The net displacement from the origin is the distance travelled, therefore 0 distance travelled results in a 0 velocity.

now average speed (which is a scalar) is (10 X 3.1416 X 51.3 metres)/(6mins X60 secs/min)=4.4686 metres/sec and is independent of the net displacement from the origin (think of it like a speedometer)

so no puzzle here
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Old 22nd September 2007, 06:46 AM   #3
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Default Re: Physics puzzle

Quote:
Originally posted by star882
There is a circular running track 168 feet in diameter. Peggy Liska runs 10 laps around the track in 6 minutes. What is her average velocity in meters per second?
168' = 51.2064 m
perimter = 160.86965 m
10 laps = 1608.6965 m
1608.7/360 sec = 4.4686 m/s is her speed...

but (just asking the question one knows there has to be a but...) end - start = 0 (because it is a circular track and she traveled an integer number of laps start = end) so avaege velocity is 0m/s

dave
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Old 22nd September 2007, 06:48 AM   #4
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Stew, t may seem i posted way after you, but ibecause of the way i browse the forum, i did not see your answer ... honest. (i go thru the list of new posts and open them in tabs and then slowly go thru them0

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Old 22nd September 2007, 07:29 AM   #5
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But would she take off?
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Old 22nd September 2007, 07:48 AM   #6
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Quote:
Originally posted by pinkmouse
But would she take off?
What did she take off?
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Old 22nd September 2007, 08:15 AM   #7
Nanook is offline Nanook  Canada
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Default np Dave...

the thing here is that it must be understood the difference between a vector (like velocity) and a scalar (like speed).

Of course some really interesting things happen when you do vector calculus...and end up with a scalar

for those that may not know the difference:

A vector has direction and magnitude, while a scalar does not (say like temperature or speed). scalar addition behave like normal "math", vector addition is the sum of all magnitudes and all directions...
Vector or "triangular" addition is unique to vectors.

so Dave, the average velocity is zero, while the average speed is 4.4686 m/s
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Old 22nd September 2007, 08:17 AM   #8
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Quote:
Originally posted by Geek
What did she take off?
Sorry, I'll clarify - would she get airborne.
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Old 22nd September 2007, 08:25 AM   #9
Nordic is offline Nordic  South Africa
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But, does it blend?
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Old 23rd September 2007, 12:33 AM   #10
Nanook is offline Nanook  Canada
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Default airborne and blending?

Pinkmouse:well if she was a huge mass and expelled or "voided' a large percentage of her mass long enough to create momentum (essentially the burn rate to rocket scientists), then she would. Her momentum would have to overcome the earth's gravitational field

Nordic: scalars and vectors don't "blend". you can operate on scalars using vector calculus, the end result would be a vector field. That's what a "gradient" is , a vector field showing the change in scalars, with respect to a displacement (a vector)



a nice explaination is here
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