the clock at the capitol building has an hour hand that is 12 feet long.how many feet will the top of the hand move between the hours of the midnight and 8am?
To determine how many feet the top of the hour hand of the clock at the Capitol building moves between midnight and 8 am, we need to calculate the distance it travels for each hour.
The formula to calculate the distance traveled by the tip of the hour hand is:
Distance = (Hour / 12) * Circumference of the circle covered by the hour hand.
Let’s start by calculating the circumference of the circle covered by the hour hand. The circumference of a circle with a radius (length of the hour hand) is given by the formula:
C = 2 * π * Radius
Given that the length of the hour hand is 12 feet, we can calculate the circumference as follows:
C = 2 * π * 12 feet
Next, let's calculate the distance moved by the hour hand for each hour between midnight and 8 am:
Distance at 1 am = (1 / 12) * C
Distance at 2 am = (2 / 12) * C
Distance at 3 am = (3 / 12) * C
Distance at 4 am = (4 / 12) * C
Distance at 5 am = (5 / 12) * C
Distance at 6 am = (6 / 12) * C
Distance at 7 am = (7 / 12) * C
Distance at 8 am = (8 / 12) * C
Finally, to find the total distance moved between midnight and 8 am, we sum up the distances for each hour:
Total Distance = Distance at 1 am + Distance at 2 am + ... + Distance at 8 am
Now you can substitute the calculated values into the formulas and carry out the calculations to find the answer.