Question

The second hand on Mr. Vidler's Alarm Clock is 6 cm long. Approximately how far does the tip travel in 5 minutes and 15 seconds? [Round your answer to the nearest tenth. Only type in the number, no units.]

Answer 1

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