A space station consists of two donut-shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.30 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

Question

A space station consists of two donut-shaped living chambers, A and B, that have the radii shown in the drawing. As the station rotates, an astronaut in chamber A is moved 2.30  102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

anonymous · Answer

I've attached the picture for this.  Someone please help!

anonymous · Answer

You can figure this one one in so many ways. Let's start with the easiest one.

what you are given are 2 radii that each represent the distance of the chambers from the center of the station. Since the station is rotating astronauts inside are rotating as well, making circles. circumference of these circles is O = 2rPI

So, you can calculate what percentage of his circle the astronaut at point A passed (when he passed 2.3*10^2), and that percentage is the same as the percentage of the circumference the astronaut at point B passed around his circle. 

So you have 
$$O_1=2r_1\pi$$$$O_2=2r_2\pi$$ 
Now we know that $$\frac{s_1}{O_1}=\frac{s_2}{O_2}$$

Solve for $$s_2$$
and simplify (you will loose 2s and Pis)
and you get $$s_2=\frac{r_2}{r_1}s_1$$

where s is distance passed and r is radius

anonymous · Answer

Got it!  Its 790.6 meters!  Thank you, thank you!