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 62.0kg and he a mass of 72.0kg, and they start from rest 15.0m apart.

(A)Find his initial acceleration.

(B)Find her initial acceleration.

(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?
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Explanation / Answer

Fix the frame of reference on the boy. Consider the direction of motion of the woman as positive. In this frame of reference, for the woman: - Initial velocity u = 0 Acceleration a = 1.62×10^-11 + 1.43×10^-11 = 3.05 * 10^-11 m/s^2 Displacement S = 17.0 m Time taken t = ? S = ut + 1/2 at^2 17 = 0 + 1/2 * 3.05 * 10^-11 * t^2 17 = 1.525 * 10^-11 t^2 t^2 = 17/(1.525 * 10^-11) t^2 = 11.147541 * 10^11 t^2 = 1.1147541 * 10^12 t = sqrt(1.1147541 * 10^12) = 1.056 * 10^6 s = 1.056 * 10^6/(24*3600) days = 12.2 days Ans: 12.2 days

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