in outer space with no external forces on a rocket the unlimate rocket engine is

Question

in outer space with no external forces on a rocket the unlimate rocket engine is an ion engine where matter is ionized and accelerated to extremely high speed by a large voltage difference calculate the approximatelu how fast a 100kg rocket will ultimately go if 2kg of its mass where hydrogen which was completely ionized andd acclereted through a potential difference 30kv. Give your answer in kilometers per hour. Integrate 0=m.dv-vex.dm and calculate hydrogens's speed using: 1/2 m v^2= q.V, where q=1.6x10^-19C and m=1.67x10^-27kg

Explanation / Answer

from formula 1/2 m v^2 = q.V

1/2(1.67x10^-27xv^2) = 1.6x10^-19x30x10^3

v = sqrt[(2x1.6x10^-19x30x10^3)/(1.67x10^-27)]

so, v = 2.4 x 10^6 m/s

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