# Quick question on Newton's third law & energy conservation

1. Mar 10, 2013

### DavidDoakes

I have a quick question on Newton's third law.

When a 100kg astronaut in space is holding a 100 kg rock and then pushes it away from him with 50 joules of energy (the kinetic energy put into the system) and a second astronaut (observer) is watching, sitting still relatively to the location where the other astronaut was holding the rock and generating the 50 joules before the push, does the observer see the rock float to the left of him with 1 m/s and the astronaut float to the right of him with 1 m/s or does he see the rock float to the left with 0.707 m/s and the astronaut to the right with 0.707 m/s? In other words, is the total kinetic energy he observes equal to 100 joules or 50 joules?

2. Mar 10, 2013

### Staff: Mentor

Hi DavidDoakes, welcome to PF!
Energy is conserved. What does that imply for your question?

3. Mar 10, 2013

### DavidDoakes

I'd say both the astronaut and rock would have speeds of 0.707 m/s relative to the observer (otherwise you can could catch both the astronaut's and the rock's kinetic energy, transport it to the center of the system and use half of it to repeat the whole thing, gaining 50 joules of free energy every time), but there are so many (popular) sources out there that explain it like they would have speeds of 1 m/s relative to the observer, so I was wondering if I missed something.

4. Mar 10, 2013