An astronaut is on a 100-m lifeline outside a spaceship,circling the ship with an angular speed of 0.100 rad/s.How far inward can she be pulled before the centripetal acceleration reaches 5g = 49 m/s²? A)10.1 m B)50.0 m C)72.7 m D)89.9 m

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Quizplus · Accepted Answer

The centripetal acceleration is given by $ a_c = \omega^2 \times r $. Setting $ a_c = 49 \, \text{m/s}^2 $ and $ \omega = 0.100 \, \text{rad/s} $, solve for $ r $: $ r = \frac{49}{(0.100)^2} = 4900 \, \text{m} $. The initial radius is 100 m, so the inward distance is $ 100 - \frac{49}{(0.100)^2} = 72.7 \, \text{m} $.

An Astronaut Is on a 100-M Lifeline Outside a Spaceship,circling