ANSWERS TO PROBLEMS
First, mechanical energy drives the car’s electric generator. Second, the electrical energy is converted into chemical energy when the battery is recharged.
From the kinetic energy equation we get
v = √(2 E/m)
Since the engine is 25% efficient, the energy available to propel the car is 48,000 × 0.25 or 12,000 joules. So
v = √(24,000/1,000) = 2√6 = 4.9 meters per second
e = (300 - 20)/300 = 14/15 = 0.93 = 93%
The crossover point, t, in hours is found by equating the nuclear power plant mass and that of the fuel cell with its associated fuel. The equation is
1000 = 50 + 25 + ½t t = 1850 hours = 77 days
E = ½ mv² = (10⁶(0.9 × 3 × 10⁸)²)/2 = 3.6 × 10²² joules
The ship will use the same amount of energy to decelerate at its destination. Note that this calculation assumes a perfect efficiency in converting the energy of matter annihilation into the kinetic energy of the space ship. The mass consumed is
m = E/c² = (3.6 × 10²²)/(9 × 10¹⁶) = 4.0 × 10⁵ kg
almost half the spaceship mass.