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Question
The length of a clock's minute hand is 15 cm. Calculate the distance traveled by its tip in

a) 1 hour
b) 2 hours 30 minutes
c) 45 minutes
d) 1 minute


- For 1 hour, I got 94.2 cm
- For 2 hours 30 minutes, I got 235.5 cm
- For 45 minutes, I got 79.2 cm
- I did not get the distance traveled for 1 minute

I am unsure if any of these answers are correct. Also, is the clock's minute hand the radius of the clock?
Thanks

Answer
The first 2 are correct so it seems to me that you have figured out that the distance the tip travels L = (circumference)x(fraction of an hour of elapsed time) = (2pi・r)・(f), where r = length of minute hand = 15 (= radius of circle it describes), f = (given hours)/1 hour.

For a), f = 1

b) f = 2.5

c) f = 45 min/60 min = 0.75 -> L = (2pi)r(0.75) = 70.7 cm (different from your answer)

d) f = 1 min/60 min = 0.017 -> L = 1.57 cm

Another way to calculate c) is to write L = (2pi)(15)(45/60) = (2pi)(15)(3/4) = 1.57.

The minute hand doesn't have to be the radius of the clock since the radius of the clock is not used in the problem. To make a nice looking clock, you would probably want the minute hand to be slightly less than the radius of the clock, but this is only for aesthetics and does not affect the calculation.

Randy

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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