The tip of the minute hand of Boston's Custom House Tower clock travels 6ft. 10 in. in 5 minutes.How long is the minute hand ?
5 minutes is 1/12 of a rotation
so
(1/12)(2pi r) = 82 inches
r = 82(12)/(2pi)
= you do the button-pushing
To find the length of the minute hand, we can divide the distance traveled in 5 minutes by the time taken. Here's how you can do it:
1. Convert the 6ft 10in distance traveled in 5 minutes to a single unit. Since there are 12 inches in a foot, we can convert the 6ft 10in to 6.8333 feet.
- 6ft 10in = 6 + (10/12) = 6.8333 feet
2. Divide the total distance traveled by the time taken:
- Length of minute hand = Distance traveled / Time taken
- Length of minute hand = 6.8333 feet / 5 minutes
3. Calculate the length of the minute hand:
- Length of minute hand = 1.3666 feet per minute x 60 minutes (to convert from feet per minute to feet per hour)
- Length of minute hand = 82 feet
Therefore, the length of Boston's Custom House Tower clock's minute hand is 82 feet.