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.

a) Find His initial acceleration

b) Find Her initial Acceleraion

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.)

d) Would their acceleration, in fact, remain constant?

Explanation / Answer

The gravitational force of attraction is given by:

F = GM1M2/r^2 (G = gravitational constant, M1 and M2 are masses, r = distance between masses)

F1 = M1a1 (Newtons second law)

M1a1 = GM1M2/r^2

a1 = GM2/r^2 = his initial acceleration

F2 = M2a2

M2a2 = GM1M2.r^2

a2 = GM1/r^2 = her initial acceleration

his acceleration = a1 = G*60/17^2 = 6.673*10^-11*60/17^2 = 1.38*10^-11 m/s^2

a1 = 1.38*10^(-11) m/s^2 = answer a)

her acceleration = a2 = G*70/17^2 = 6.673*10^-11*70/17^2 = 1.616*10^-11 m/s^2

a2 = 1.616*10^-11 m/s^2 = = answer b)

Total acceleration = 3*10^-11 m/s^2

Distance = 17 m

Using s = ut + (1/2)a*t^2

17 = (1/2)*3*10^-11*t^2

t = sqrt(17/((1/2)*3*10^-11))

t = 1.064*10^6 s

t = 12.31 days

t = 12.3 days = answer c)

F is inversely proportional to the square of distance between them, so the acceleration will increse as r decreases.

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