Question

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 3:35 to 3:55? (Hint: Find the number of degrees per minute first.) Part 2: How far does the tip of the minute hand travel during that time? You must show all of your work

Answer 1

Part 1. Imagine a clock without the hour hand, When clock strikes 3:35, the minute hand is at 7. When it strikes 3:55, the minute hand is in 11. Each gap between two adjacent digits in the clock measures 30°. This is because a revolution divided by 12 is 360/12 = 30. Then, the angle between the minute hands in the picture is equal to 4(30°) = 120°. Know that π radians is equal to 180°. Converting 120° to radians,

120°(π radians/180°) = (2/3)π or 2.09 radians

Part 2. For this part, we determine the arc length intercepted by the angle 120° because this is the total distance travelled by the tip of the minute hand.

S = rθ, where θ is the angle in radians and r is the radius of the circle represented by the minute hand.
S = (4)(2.09)
S = 8.36 inches

Hence, the tip of the minute hand travelled a total distance of 8.36 inches.