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I have a question that has been really been bothering me, even after my teacher spent awhile trying to discuss it. The question was:

A 5.0e4 kg space probe is traveling at a speed of 11,000 m/s through space. Rockets are fired along the line of motion in order to reduce the probe's speed. The rockets generate a force of 4.0e5 N over a distance of 2500km. What is the final speed of the probe?

My answer (incorrect according to teacher) was this:

using W=Fdx (W=KE) KE=(4e5 N)(2500000m)=1e12 J (amount of Joules used to change rocket speed)

KE=.5mv^2 so 1e12 J=(.5)(5e4 kg)(v^2) v=6325 m/s (change in velocity)

SO: 11,000 m/s - 6,325 m/s = 4675 m/s Final Speed

My teacher's explanation was this:

1e12 J (same as above -- amount of Joules used to change rocket speed)

For ship itself: KE=(.5)(5e4 kg)(11,000^2) 3.025e12 J

3.025 J - 1e12 J = 2.025e12 J

2.025e12 J = (.5)(5e4 kg)(v^2) V = 9000 m/s Final Speed

After looking over this answer, it has made me VERY confused about why mine didn't work, and I'll support my explanation:

When moving in space, velocity can only be measured in comparison to other objects that are considered to have no velocity. Because of this, the amount of kinetic energy put into it, and its corresponding velocity, could be the only thing used to measure a change in velocity.

For example: Say you have 2 ships seemingly moving at eachother. In reality, you are moving towards the ship at 11,000 m/s, while the other ship is stationary. However, it appears from your point of view that you are actually stationary, instead, and that the other ship is moving towards you. You know that the ship can only withstand a collision at 6,000 m/s, so you must compensate by propelling yourself up to 5,000 m/s away from the ship, with KE=(.5)(5e4)(5,000^2) = 6.25e11 J. However, according to my teacher's theory, this would not work, because you are actually moving at 11,000 m/s, or (.5)(5e4)(11,000^2) = 3.025e12 .

Using the same amount of KE found by a "still" ship, you would do 3.025e12 - 6.25e11 = 2.375e12 J SO 2.375e12=(.5)(5e4)(v^2) v=9,747 m/s, or a change of 1,253 m/s.

As you saw above, the numbers come out differently once again, depending on who's actually moving. However, when your in space, it should not matter whether you are moving at 11,000 and the other ship is still, or vice versa, the velocity change should still come out the same, correct?

Quickly, here's another example of my teacher's theory that I'm having trouble with:

Say you are in a stationary car with a mass of 1kg (to keep it simple), and want to move 1 m/s with respect to the ground. You would need (.5)(1)(1^2) = .5 J of energy in the car to get it moving at that speed. HOWEVER, take into consideration the fact that the Earth is spinning. We will say, spinning at 500 m/s. This means you actually want to go 501m/s to move 1 m/s with respect to the ground. because of this, you would ACTUALLY need (.5)(1)(501^2)= 125500.5 m/s MINUS the kinetic energy you already have when you were traveling with the Earth: (.5)(1)(500^2) = 125000. 125500.5-125000 = 500.5 J you ACTUALLY need to move 1 m/s, not .5 m/s.

Thanks for your help!