Answer:
v = 5.88 10⁷ m / s
Explanation:
For this exercise we use the relation
E = m c²
also indicate that all energy is converted into kinetic energy
E = K = ½ (M-2m) v²
where m is the mass of antimatter and M is the mass of the ship's mass. Factor two is due to the fact that equal amounts of matter and antimatter must be combined
we substitute
m c² = ½ (M-2m) v²
v² = [tex]2 \frac{m}{M+2m} \ c^2[/tex]
let's calculate
v = [tex]\sqrt{2 \ \frac{4 \ 10^4 }{2 \ 10^6 + 2 \ 4 \ 10^4} \ (3 \ 10^8)^2}[/tex]
v = [tex]\sqrt{ 34.615 \ 10^{14}}[/tex]
v = 5.88 10⁷ m / s