It doesn’t matter to from what reference the velocity is measured. Let’s say we have a rocket with a mass of 10,000 kg and moving 8,000 m/s relative to some external reference point. Its momentum and kinetic energy are,
P = mv = 10,000*8,000 = 8E+7 kg-m/s
KE = 0.5mv^2 = 0.5*10,000*8,000^2 = 3.2E+11 J.
Let’s say the rocket expels 1,000 kg of propellant at –3,000 m/s relative to the rocket. To make the math simple, let’s say the propellant is expelled instantaneously rather than over a period of time. Relative to the original reference point, the expelled propellant is moving 5,000 m/s; therefore its momentum and kinetic energy are,
P = mv = 1,000*5,000 = 5E+6 kg-m/s
KE = 0.5mv^2 = 0.5*1,000*5,000^2 = 1.25E+10 J.
Since momentum is conserved the, the final momentum of the rocket must be the initial momentum less that of the propellant,
P = 8E+7 – 5E+6 = 7.5E+7 kg-m/s.
Therefore the rocket’s final velocity is,
v = P/m = 7.5E+7/(10,000–1,000) = 8,333.3 m/s
and the change in velocity is,
delta-V = 8,333.3 – 8,000 = 333.3 m/s.
The rocket’s kinetic energy is now,
KE = 0.5mv^2 = 0.5*9,000*8,333.3^2 = 3.125E+11 J.
The total final kinetic energy is that of the expelled propellant plus rocket,
KE = 1.25E+10 + 3.125E+11 = 3.25E+11 J
thus the change in kinetic energy is,
delta-KE = 3.25E+11 – 3.2E+11 = 5E+9 J.
Let’s now perform the exact same calculation but measuring velocities from a reference point moving along with the rocket at its initial velocity. The rocket’s initial velocity in this reference frame is zero, thus its momentum and kinetic energy are both zero.
In relation to our new reference point, the expelled propellant is moving –3,000 m/s, thus its momentum and velocity are,
P = mv = 1,000*(–3,000) = –3E+6 kg-m/s
KE = 0.5mv^2 = 0.5*1,000*(–3,000)^2 = 4.5E+9 J.
The final momentum of the rocket is,
P = 0 – (–1 3E+6) = 3E+6 kg-m/s
therefore it’s final velocity is,
v = P/m = 3E+6/(10,000–1,000) = 333.3 m/s.
Since the initial velocity was zero, the delta-v is also 333.3 m/s, which is the same change in velocity as determined in the first calculation.
Let’s now calculate the kinetic energy of the rocket,
KE = 0.5mv^2 = 0.5*9,000*333.3^2 = 5E+8 J
thus the total kinetic energy of propellant plus rocket is,
KE = 4.5E+9 + 5E+8 = 5E+9 J.
And since we started out with zero kinetic energy, 5E+9 J is also represents delta-KE. We therefore see the exact same change in energy as in the previous calculation. It made no difference from which reference point we measured the velocities.