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**1) A spaceship has a mass of 20000kg. It has a matter-anti-matter engine which can transform the annihilation energy into kinetic energy of the spaceship with an efficiency of 5%. How many grams of matter and anti-matter do you need to take the ship completely out of the influence of the earth's gravitational force (achieving escape velocity)?**

My Guess:

The escape velocity on the surface of the earth is 11200m/s

Let M be mass of rocket

m be mass of antimatter

K be kinetic energy

K=(gamma-1)Mc^2 (then I substitute the values 11200m/s, etc. into this formula)

I get K=1.26x10^12 J

Now set K=0.05*(2mc^2) and solve for m gives me the answer, AM I RIGHT? Is this the correct way to solve this problem?? I am really not sure...

Also, I have some trouble understanding the scenario, so I am really not sure if I have done the calculations correctly:

Is the engine turned off at the moment it leaves the earth's surface or is it on all the way (i.e. annihilation never stops?) ?

Is the spaceship continuously losing mass due to the annihilation reaction? If so, how can I take this into account in my calculations?

For the matter/antimatter, how can I find the kinetic energy

*before*the collision of the matter/anti-matter?

By the way, the total (relativistic) energy is defined to be equal to kinetic energy + rest energy. But how come there is no potential energy? For example, why is the gravitational potential energy not taken into account for the equation of total (relativistic) energy?

Thanks for your help!