Question

A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. She has a mass of 62.0 kg and he a mass of 70.0 kg , and they start from rest 23.0 mapart.

a) Find his initial acceleration

b) Find her initial acceleration

c) If the astronauts' acceleration remained constand, how many days would they have to wait before reaching each other?

Answer 1

use g = GM/r^2 where g is the acceleration of the object M is the mass of the other object r is the distance between

them and G is 6.67300 × 10^-11 m3 kg-1 s-2

a)

g = (6.673 x 10^-11 x 62) / 23^2

g = 7.82 x 10^-12 m/s^2

b)

g = (6.673 x 10^-11 x 70) / 23^2

g = 8.83 x 10^-12 m/s^2

c)

there total acceleration towards one another will just be the individuals added together

= 1.665 x 10^-11 m/s^2

then we just use kinematic equation d = vi*t + 1/2*a*t where the Vi is 0

23 = 1/2 * 1.665 x 10^-11 x t^2

t = 1662156 seconds

t = 19.2379 days