Refer to the diagram shown below.
The relative velocity before the collision is 0.15 m/s. Therefore consider one satellite to be at rest and the other satellite to have a velocity of 0.15 m/s.
The total momentum before impact is
P₁ = (4000 kg)*(0.15 m/s) = 600 kg-(m/s)
After elastic impact, the rebound velocities are 0.15 m/s and u m/s.
The total momentum after impact is
P₂ = (4000 kg)*(-0.15 m/s) + (7500 kg)*(u m/s) = -600 + 7500u kg-(m/s)
Because momentum is conserved, therefore
-600 + 7500u = 600
u = 1200*7500 = 0.16 m/s
The relative velocity after impact is
0.16 - (-0.15) = 0.31 m/s
Note: In elastic impact, there is no loss of kinetic energy.
Answer: 0.31 m/s
