How far along circular arch is an astronaut

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An astronaut in chamber A moves along a circular arc of 240 meters, while the radius of chamber A is 320 meters and chamber B is 1100 meters. The relationship between the arc lengths can be determined using the formula for arc length, s = θ × r, where θ is the angle in radians. By finding the angle θ for chamber A, it can be applied to chamber B to calculate the corresponding arc length. The discussion highlights the importance of using the correct formulas in physics to ensure accurate results. Understanding the relationship between the two chambers through proportional reasoning and arc length formulas is crucial for solving the problem.
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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?


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

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