One Hand One
How far does thepoint of each hand travel in one day?
The hands of a clock vary in length. If the hour handis 4 inches long, the monute hand 6 inches long, and the second hand 7 inches long, how far does this of each hand travel?
and also how many feet does the second hand travel in 24 hours, how many miles?
I thought so hard about how to go about this problem, and got no where, so if any one can help me through it, or even start me out on it , that would be awsome thanks so much!
Let;s think about how long it takes each hand to go round the clock face.
The hour hand takes 12 hours to go right round the clock face. It therefore does 2 laps of the clockface per day. How far does it travel doing one lap? Well, it’s the circumference of a circle, with radius equal to the length of the hand. The circumference of a circle is C = 2πr. In the case of the hour hand, which is 4 inches long, the circumference is 2*π*4 = 25.1 inches. So the tip of the hour hand travels a distance of 25.1 inches when travelling a single lap. We know it travels 2 laps, or 50.3 inches, in a day.
What about the minute hand? it takes 1 hour to go right round the clockface, so it does 24 laps of the clockface per day. The distance it travels per lap is 2*π*6 = 37.7 inches per lap, and therefore the distance it travels per day is 24*37.7 = 905 inches per day.
Now we come to the second hand. It takes 1 minute to go right round the clockface, so it does 1440 laps of the clockface per day. The distance it travels per lap is 2*π*7 = 44.0 inches per lap. Therefore the distance it travels per day is 44.0*1440 = 63334.5 inches per day.
We know there are 12 inches in a foot, so the distance in feet it travels per day is 63334.5/12 = 5277.9 feet. And there are 5280 feet in a mile, so the number of miles per day it travels is 5277.9/5280 = 1 mile.
West Side Story-One Hand, One Heart