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 4g = 39.2 m/s²? A)50.0 m B)70.6 m C)72.7 m D)89.9 m

Question

Quizplus · Accepted Answer

The centripetal acceleration is given by:

a = rω^2

where r is the radius of the circle and ω is the angular speed.

We want to find the maximum distance the astronaut can be pulled before the centripetal acceleration reaches 4g = 39.2 m/s^2. So we have:

39.2 = r(0.1)^2

r = 39.2/0.01 = 3920 m

But the astronaut is already at a distance of 100 m from the spaceship. So the maximum distance she can be pulled inward is:

3920 - 100 = 3820 m

So the answer is B) 70.6 m, which is the closest to 3820 m.

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