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 64.0 kg and he a mass of 76.0 kg , and they start from rest 15.0 m apart.

Find his initial accel..

Find her initial accel

If the astronauts' acceleration remained constant, how many days would they have to wait before reaching each other? (Careful! They both have acceleration toward each other.)

If you could help me/show me how you do it... that would be great

Answer 1

Step-by-step explanation:

In space , there will be no gravitational force except mutual attraction due to gravitational attractive force

Force of gravity between them

= GMm / r²

M = 64 kg , m = 76 kg , r = mutual separation = 15 m

G = 6.67 x 10⁻¹¹

Force of mutual attraction = (6.67 x 10⁻¹¹ x 76 x 64) / 15²

= 144.2 x 10⁻¹¹ N. This force will act on each of them .

initial acceleration on man = force / mass

= 144.2 x 10⁻¹¹ / 76

= 1.897 x 10⁻¹¹ m /s²

initial acceleration on woman = force / mass

= 144.2 x 10⁻¹¹ / 64

= 2.253 x 10⁻¹¹ m /s²

Relative acceleration

= (1.897 x 10⁻¹¹ +2.253 x 10⁻¹¹)

= 4.15 x 10⁻¹¹ m /s²

distance to be covered s = 15 m

s = 1/2 at² , a = mutual acceleration = 4.15 x 10⁻¹¹ m /s²

t = √(2s/a )

= √(2x15) / (4.15 x 10⁻¹⁵ )

= 8.5 x 10⁷ s

= 85 x 10⁶ / (24 x 60 x 60 ) days

= 983.8 days .