Answer
The total mass of matter and antimatter required is $1.35\times 10^4~kg$
Work Step by Step
We can find the kinetic energy of the starship:
$K = (\gamma-1)mc^2$
$K = (\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)mc^2$
$K = (\frac{1}{\sqrt{1-\frac{(0.3500~c)^2}{c^2}}}-1)(2.0\times 10^5~kg)(3.0\times 10^8~m/s)^2$
$K = (1.0675-1)(2.0\times 10^5~kg)(3.0\times 10^8~m/s)^2$
$K = 1.215\times 10^{21}~J$
We can find the total mass $M$ of matter and antimatter required to produce this amount of energy:
$E = Mc^2$
$M = \frac{E}{c^2}$
$M = \frac{1.215\times 10^{21}~J}{(3.0\times 10^8~m/s)^2}$
$M = 1.35\times 10^4~kg$
The total mass of matter and antimatter required is $1.35\times 10^4~kg$.
