Two manned satellites approaching one another, at a relative speed of $0\mathrm{.}150$ m$/$s$,$ intending to dock. The first has a mass of $3\mathrm{.}00103$ kg$,$ and the second a mass of $7\mathrm{.}50103$ kg$.$

$($a$)$

Calculate the final velocity $($after docking$)$ in m$/$s by using the frame of reference in which the first satellite was originally at rest. $($Assume the second satellite moves in the positive direction. Include the sign of the value in your answer.$)$

m$/$s

$($b$)$

What is the loss of kinetic energy $($in J$)$ in this inelastic collision?

J

$($c$)$

Repeat both parts by using the frame of reference in which the second satellite was originally at rest.

final velocity $($m$/$s$)$

m$/$s

loss of kinetic energy $($J$)$

J

Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.