Answer: 3.297 centimeters.
Step-by-step explanation:
First, remember that if we have a circle of radius R, and we have an arc of angle A, the length of this arc is:
L = (A/360°)*2*3.14*R
In this case, we can think on a circle of radius R = 6cm.
And the angle in this case will be an angle of 5 minutes and 15 seconds.
We know that a clock does a complete revolution in 60 minutes, then:
60 minutes = 360°
First, we need to write 5 minutes and 15 seconds in minutes only.
we know that 60 seconds = 1min
then:
1 = 1min/60seconds = (1/60) min/seconds
then:
15 seconds = 15 seconds*((1/60) min/seconds) = (15/60) min = 0.25 min
Then:
5 minutes and 15 seconds = 5 min + 0.25 min = 5.25 min
Now we can use the relationship:
60 minutes = 360°
then:
1 = 360°/60min
Then:
5.25min = (5.25min)*(360°/60min) = 31.5°
Then we have A = 31.5°
Then the length of this arc (that is the distance that the tip of the tip travels in 5 minutes and 15 seconds) is:
L = (31.5°/360°)*2*3.14*6cm = 3.297 cm
