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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

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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