91Ó°ÊÓ

The 'impulse' refers to the change in momentum of the system. The provided impulse value is \(350-\mathrm{N} \cdot s\). This impulse is equal to the change in momentum for the system (satellite and booster rocket); thus, we can see that their total momentum before the explosion/detachment is zero (as they are one system and not moving), and after the explosion/detachment, their total momentum is equal to the change in momentum caused by the impulse.

Because there are no external forces involved, the momentum after the explosion should still remain zero. However, this momentum is now divided between the satellite and the rocket. They move in opposite directions, so if we assume that the rocket moves in the positive direction, then the satellite moves in the 'negative' direction. According to the conservation of momentum, the satellite's momentum plus the rocket's momentum equals zero, or in other words, their momenta are equal in magnitude but opposite in direction. Hence, the total momentum after separation is \(350 \mathrm{N.s}\). If we denote \(v\) as the common (relative) speed of the satellite and the rocket, we have the equations: \(Momentum_{satellite} = Momentum_{rocket}\) and \(950kg*v + -640kg*v = 350 \mathrm{N.s}\).

To get the relative velocity, you rearrange the equation: \(950kg*v + -640kg*v = 350 \mathrm{N.s}\) for \(v\). You get \(v = \frac{350 \mathrm{N.s}}{950 \mathrm{kg} + 640 \mathrm{kg}}\). Now you can calculate the relative speed to be approximately \(0.23 \mathrm{m/s}\).