# Calculating the mass of matter required to accelerate a spaceship

1. Apr 2, 2013

### dylhynes

1. The problem statement, all variables and given/known data
A spaceship is powered by a matter-antimatter reactor. Suppose you have a 23000-metric-ton spaceship and wish to accelerate it to 0.03 c. What is the total mass of matter and anti matter required, assuming a 100 % efficient engine.

2. Relevant equations
Really not sure about this question, but thinking that E=mc^2 and F=ma will be used somewhere

3. The attempt at a solution
Not sure how to approach this problem, any help would be greatly appreciated.

2. Apr 2, 2013

### voko

You are right about $E = mc^2$. This gives you the amount of matter/anti-matter one needs to annihilate to obtain energy $E$. However, $F = ma$ is not good - it is only valid for slow motion, and 0.03 c may be too high for it. Instead, consider the relativistic kinetic energy of some mass M moving at 0.03 c.

3. Apr 2, 2013

### dylhynes

Ahh, I understand what I did wrong now. I overlooked the fact that the spaceship only has kinetic energy while it is travelling. I solved for KE, then plugged that back into E=mc2. Rearranging for m I got the answer of 1.0x104 kg, which was correct. Thank you very much. Also if you don't mind answering, how did you type those equations in that math font ? I am new here.

4. Apr 2, 2013

### voko

Hit the quote button my message, and see the code for that. While you are there, click the $\Sigma$ symbol at the top right of the text box, it will have a reference for much more.

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