Question

How far does the tip of the minute hand of a clock move in 1 hour and 27 minutes if the hand is 2 inches long?

Answer 1

Convert 27 minutes to hours first:
\[\#hours = 27 minutes \times \frac{1 hour}{60 minutes}=0.45hours\]
So in total, 1 hour 27 minutes = 1.45 hours.

Notice that in 1 hour, the minute hand will move through a full circumference of the clock face. In 1.45 hours, the minute hand will move through 1.45 circumferences.

So you need to find out how long 1 circumference is, using \[circumference=\tau \times r = 2 \pi r\], and then find out how long 1.45 circumferences are.

Answer 2

find the angle the hand moves through in radians:
2pi+(27/60)(2pi)=2.9pi Radians
arc length=(theta)(radius) where theta is in radians
2.9x2xpi=5.8xpi inches

Answer 3

angle(in radians) * radius = arc length

in 1 hour and 27 minutes the clock does angle of :
1 hour = 360 degrees
27 minutes = 162 degrees

360 in radians is 2pi
162 in radians is 0.9pi

2pi + 0.9pi = 2.9pi radians

2.9*2 = 5.8pi inches

Answer 4

thank you all