A couple of astronauts agree to rendezvous in space after hours. Their plan is t

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 60.0 kg and he a mass of 70.0 kg , and they start from rest 17.0 m apart.

Part A) Find his initial acceleration.

Part B) Find her initial acceleration.

Part C) 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.)

Part D) Would their acceleration, in fact, remain constant?

Explanation / Answer

Let her mass, m1 = 60 kg

his mass, m2 = 70 kg

A) Force between them, F = G*m1*m2/r^2

his initial acceleration = F/m2

= G*m1/r^2

= 6.67*10^-11*60/17^2

= 1.38*10^-11 m/s^2

B) her initial acceleration = F/m1

= G*m1/r^2

= 6.67*10^-11*70/17^2

= 1.615*10^-11 m/s^2

C) let t is the time taken

d = d1 + d2

17 = 0.5*1.38*10^-11*t^2 + 0.5*1.615*10^-11*t^2

t = sqrt(2*17/(1.38*10^-11 + 1.615*10^-11))

= 1065469 s

= 1065469/(24*60*60)

= 12.33 days

4) No. As the distance decreses betwenn them force increases and acceleration also increses.

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