A 900-kg two-stage rocket is traveling at a speed of 6.50 x 10^3 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a relative speed (relative to each other) of 2.80 x 10^3 m/s along the original line of motion. a) What is the speed and direction of each segment after the explosion? b) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]
E = K + U = (.5)mv^2 + mgy
The Attempt at a Solution
This doesn't look like too difficult a problem, but I'm confused by the wording that the text here uses. Specifically, the part where it says that their speed in relation to each other is 2.80 x 10^3 m/s which is slower than they were both moving a moment ago. If an explosion has separated the rocket into two pieces, wouldn't one be moving more quickly and the other be moving more slowly? Is it trying to say that one piece is now moving 1.40 x 10^3 m/s faster and the other is moving 1.40 x 10^3 m/s slower (this is all I could come up with)? Similarly, if they're both moving at that speed along the original line of motion, why does it ask for the direction of their motion as well? I don't see any indication in the problem that either piece has changed course... I'm sure it can't be too difficult a problem, but I really wish there had been some kind of accompanying diagram. If anyone could help by writing this out in a way I could understand it (or drawing it if it'd be easier) I'd be a happy camper.