PLEASE EXPLAIN THE VARIABLES IN YOUR FORMULAS. ALSO PLEASE DO NOT SIMPLY GUESS A

Question

PLEASE EXPLAIN THE VARIABLES IN YOUR FORMULAS. ALSO PLEASE DO NOT SIMPLY GUESS AT HOW TO SOLVE THE PROBLEM. A CONCEPTUAL EXPLANATION AND INSIGHT WOULD BE GREATLY APPRECIATED AS WELL. IF YOU DO NOT KNOW WHAT YOU ARE DOING DO NOT ANSWER. THANKS IN ADVANCE FOR THE HELP!

1) A spacecraft travels at a speed of vSE = 0.59c relative to the Earth. The spacecraft then launches a probe at speed v relative to the spacecraft (see figure below). If the probe has a speed of vPE = 0.88c relative to the Earth, what is v? c

3) A chemical reaction that produces water molecules is

2H2 + O2   ?   2H2O

This reaction releases 570 kJ for each mole of oxygen molecules that is consumed. The relativistic relation between mass and energy then implies that the mass of two hydrogen molecules plus the mass of one oxygen molecule is slightly larger than the mass of two water molecules. Find this mass difference.
kg

Explanation / Answer

1) vPE = (vSE + v)/(1 + vSe v)

0.88 = (0.59 + v)/(1 + 0.59 v)
v=0.603 c

2) KE = (gamma -1) mc^2

1.3E20 = (1/sqrt( 1- beta^2) - 1)*7400*3.0E8^2

beta = 0.548 c

3) dE = dm c^2

dm = 570.0E3/3.0E8^2= 6.33E-12 J

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