Application Two manned satellites approaching one another, at a relative speed of 0.250 m/s, intending to dock. The first has a mass of 4.00×103 kg , and the second a mass of 7.50×103 kg . (a) Calculate the final velocity (after docking) by using the frame of reference in which the first satellite was originally at rest. (b) What is the loss of kinetic energy in this inelastic collision? (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

Step-by-step solution In this problem two satellite are approaching toward one another so, calculate the final velocity when the first satellite were at rest ,and what will be the lost in the kinetic energy and then calculate the same for the second satellite ,as per the given data respectively: Step 1 of 8 (a) For an elastic collision, the momentum is conserved. Therefore, …… (1) Here is the mass of one satellite, is the mass of another satellite, is the relative velocity of first satellite before collision, is the relative velocity of second satellite before collision and is the relative velocity after collision. Step 2 of 8 Substitute in equation (1) and get: Step 3 of 8 Rearrange and solve, Therefore, the relative velocity is . Step 4 of 8 (b) The change in kinetic energy is, Here is the mass of one satellite, is the mass of another satellite, is the relative velocity of first satellite before collision and is the relative velocity of second satellite before collision.