Question

Suppose we have a spaceship about the size of a typical ocean cruise ship today, which means it has a mass of about 140 million kilograms, and we want to accelerate the ship to a speed of 11 % of the speed of light. Suppose you want to generate the energy to get it to cruising speed using matter-antimatter annihilation. How much antimatter would you need to produce and take on the ship? Express your answer using two significant figures. _____________kg

Answer 1

The mass of the ship is 1.4x10⁸ kg.

The required velocity is 0.11c = 0.11x3x10⁸ =  3.3x10⁷ m/s

The energy required to bring the ship to this velocity is 1/2mv² = 1/2x1.4x10⁸ x(3.3x10⁷)² (Since this is the kintetic energy the ship should possess at the required speed).

Energy required = 8.1675x10²² J

Collision of matter and antimatter converts all the matter into energy using the formula E = mc²

Thus, mass of both matter and antimatter required will be m = E/c² = 8.1675x10²²/(3x10⁸)² = 9.1x10⁵ kg

Only half of this is required to be antimatter. Thus, total antimatter required will be 910000/2 = 4.6x10⁵ kg