The hour hand of a clock is 3 feet long. How many feet does the tip of this hand move between 9:30 pm and 1:30 pm the following day?

Answer 1

Hi Saamarth,

This question is asking you to determine the arc length of the hour hand as it moves between 9:30 pm and 1:30 pm the following day.

The equation for arc length is (x degrees/360 degrees)*(2*pi*r), where (2*pi*r) is the circumference, and (x degrees/360 degrees) is the fraction of the circle moved by the hour hand. In this fraction, x is the angle in degrees moved by the hour hand, and r is the radius of the circle. In this case, the radius is the length of the hour hand, which is stated to be 3 ft.

To make solving the problem a little easier, we can split this calculation into 2 segments:

1) The first calculation will be the arc length when the hour hand moves from 9:30 pm to 9:30 am, which is 1 full rotation, or 360 degrees. So, the first calculation will be (360 degrees/360 degrees)*(2*pi*3 ft).

2) The second calculation will be the remaining arc length when the hour finishes moving from 9:30 am to 1:30 pm. Since each 5-minute interval is 30 degrees, 9:30 to 1:30 is 120 degrees. So, the second calculation will be (120 degrees/360 degrees)*(2*pi*3 ft).

Finally, you add these 2 calculations to find the total distance traveled by the hour hand.