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 1.99 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?
To find the distance traveled by an astronaut in chamber B during the same time, we need to know the radius of chamber B. However, the drawing or radii values are missing from the question. Without these values, we cannot provide a specific numerical answer.
However, I can still explain how to approach this problem once you have the radius of chamber B. The distance traveled along a circular arc can be calculated using the formula:
Distance = Theta * Radius
Where Theta is the angle in radians subtended by the arc, and Radius is the radius of the circular path.
To find the angle Theta for chamber A, we can use the formula:
Theta = Distance / Radius
Given that Distance for chamber A is 1.99 * 10^2 m and the radius of chamber A is given in the drawing, we can calculate Theta for chamber A.
Once we have the value of Theta for chamber A, we can use the same value to calculate the distance traveled by the astronaut in chamber B by using the formula:
Distance for chamber B = Theta * Radius of chamber B
This will give us the distance along a circular arc that an astronaut in chamber B is moved during the same time.
Remember to use consistent units (e.g., meters for distance and meters for radius) when performing the calculations.