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?

D = 72.68 m

Explanation:

given,

R = 100 m

angular speed = 0.1 rad/s

distance she can be pulled before the centripetal acceleration reaches 5g = 49 m/s².

using conservation of Angular momentum

we know,

centripetal acceleration

v = r ω

distance she has reached inward is equal to

D = 100 - 27.23

D = 72.68 m

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