The length of the hour hand of a clock is 5 inches. How long does it take for the tip to move 80 inches? Give an answer in the following form: ______ hours _____ minutes _____ seconds.

Question

I know that s=rΘ. I know that r=5 inches and that s=80 inches. I just don't know how to get an answer in radians for theta.

Answer 1

The hour hand travels 10π inches every 12 hours.

80 / 10π is 8 / π revolutions

(12)(8/π) = 30.55774907 hours

30.55774907 hours = 30 hours 33.46494442 minutes = 30 hr 33 min 27.9 sec

Answer 2

You're right...s=rθ and r = 5 inches and s=80 inches

if you divide s by r, you get θ; then θ = 80/5 = 16 rad

now, since each full rotation is 360 degrees or 2π, then

the number of rotations = 16 / 2π = 16/ (2*3.14) = 16 / 6.28 = 2.54545 rotations

each rotation represents 12 hours

so now we know we have 24 hours and 0.5454545 of 12 hours, which is 0.5454545 * 12 = 6.545 hours

so we have 30 hours and 0.5454545 of an hour, which is 0.5454545 * 60 = 32.73 minutes

so we have 30 hours, 32 minutes, and 0.72727 * 60 = 43.6 seconds

the answer is 30 hours, 32 minutes and 43.6 seconds