Question

Minute hand of a clock is 10 inches long.
how far does the tip of the minute hand move in 15 seconds?
I got that=5 pi

BUT What speed is it moving in miles/hr????



algebra - PsyDAG, Sunday, November 13, 2011 at 1:38am
Assuming it does move 5 pi, convert 5 * 3.1416 = 15.7 inches to portions of a mile. Convert 15 seconds into a portion of an hour, then increase both so divisor is a complete hour.

Thanks for your help, but I still didn't get the answer. Speed = distance/time. 5 pi is my distance, so i have to find the time. (which the answer says is 264.) I tried 15s x 1min/60s x 1hr/60min = .004166666 hr

the speed answer is 5pi/264 =approx .0575

Answer 1

The answer of 5π inches/sec is the speed of the ≤b≥second≤/b≥ hand not the minute hand like you asked for.
Is there a misprint?

The minute hand moves 6° or π/30 radians in 1 minute
so in 15 seconds, it moves 1.5° or π/120 radians

arc length = rØ = 10(π/120) = π/12 inches in 15 seconds
So in 15 seconds it would move π/12 inches

speed in inches/sec = π/180 inches/sec
(number of inches in a mile = 12(3)(1760) = 63360
number of seconds in 1 hours = 3600 )

speed in miles/hr = (π/180)(3600/63360) = π/3168
The speed of the minute hand is π/3168 mph

If you want the speed of the second hand multiply that by 60 to get the answer of 5π/264