When antimatter (which we'll learn more about in Chapter 30) interacts with an equal mass of ordinary matter, both matter and antimatter are converted completely into energy in the form of photons. In an antimatter-fueled spaceship, a staple of science fiction, the newly created photons are shot from the back of the ship, propelling it forward. Suppose such a ship has a mass of \(2.0 \times 10^{6} \mathrm{~kg}\), and carries a mass of fuel equal to \(1 \%\) of its mass, or \(1.0 \times 10^{4} \mathrm{~kg}\) of matter and an equal mass of antimatter.

a. What is the final speed of the ship, assuming it starts from rest, if all energy released in the matter-antimatter annihilation is transformed into the kinetic energy of the ship?

b. Not only do photons have energy, as you learned in Chapter 25 , they also have momentum. Explain why, when energy and momentum conservation are both considered, the final speed of the ship will be less than you calculated in part a.