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The problem on the test did NOT deal with velocities in ONE direction, but instead two: east and west. The problems found within most of the review books are with a ship traveling at some fraction of c, and then additionally, in the same direction, they fire some particles at another fraction of c; therefore, in that case, you can't just add the two values and must use that specific equation. But, that was not the type of question on the test.
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<p>It doesn't matter if the ships are going to different directions, you will still have to use the same formula. Allright then, let me try to explain it one more time and see if it will be clear this time (unlikely though as my writing skill sucks). I'm actually not sure if they are going toward each other, or moving away, but either way, the answer will still be the same.</p>
<p>Suppose they're moving apart from each other. And suppose we have a static frame of reference A, from which the speed of .6c for both ships is measured. Let's say ship 1 moves to the left, and ship 2 to the right. Since we are to assume them to move in the constant speed, it is ok to pick either ship 1 or ship 2 as the new static frame of reference. </p>
<p>Let's say, we're trying to measure the speed of ship 2 with respect to ship 1. Then we pick ship 1 as the static frame of reference. For the pilot of ship, there are two objects moving to the right direction, and they're ship 2, and frame A (which is the original frame of reference). We know the velocity of ship 2 as measured from the frame A (.6 c), and we know the velocity of frame A according to ship 1(which is also .6c). These .6c are the values of x & y. </p>
<p>That said, all you have to do is plug in .6c as x, and y values into that equation, the end result, v, will be the speed of ship 2 with respect to ship 1. As I have calculated on my previous post, the answer wouldn't be c. It would still be greater than .6c though. I don't know if anybody would even bother reading my post (I don't know if it even makes sense at all to begin with).</p>