How far along circular arch is an astronaut

[sweetwilliam]

Homework Statement

a space station consists of two donut shaped living chambers A and B, that have radii r(A)= 3.2x10^2m and r(B)=1.10x10^3m. As the station rotates, the astronaut in chamber A is moved 2.40x10^2 m along a circular arc. how far along a circular arc is an astronaut in chamber B moved during the same time?

Homework Equations

The Attempt at a Solution

i used a proportion r(A)/ circular arc = r(B)/ x and solved for x i got the correct answer but my
but i was wondering if there was a different way to solve this using formulas...my physics prof. would not be happy if i didnt use correct formulas. thanks!

 

[RTW69]

Do you remember the formula for arc length? Find θ, it will be the same for both living chambers. Do you see why your approach also works using the arc length formula?

 

[sweetwilliam]

s=theta x r i see now how that works...thanks so much, i didnt think of that at first. thanks