A spaceship flying toward the Earth at a speed of 0.5c fires a rocket at the Earth that moves
at a speed of 0.8c relative to the spaceship. What is the best approximation for the speed, v,
of the rocket relative to the Earth?
(A)v > c
(B) v = c
(C) 0.8c < v < c
(D)0.5c < v < 0.8c
(E) v < 0.5cThe most precise way to solve this problem is simply to do the math. If we let the speed of
the spaceship be u = 0.5c and the speed of the rocket relative to the spaceship be =
0.8c, then the speed, v, of the rocket relative to the Earth is
As we can see, the answer is (C). However, we could also have solved the problem by
reason alone, without the help of equations. Relative to the Earth, the rocket would be
moving faster than 0.8c, since that is the rocket’s speed relative to a spaceship that is
speeding toward the Earth. The rocket cannot move faster than the speed of light, so we
can safely infer that the speed of the rocket relative to the Earth must be somewhere
between 0.8c and c.
Mass and Energy
Mass and energy are also affected by relativistic speeds. As things get faster, they also get
heavier. An object with mass at rest will have a mass m when observed to be traveling
at speed v:
Kinetic Energy
Because the mass increases, the kinetic energy of objects at high velocities also increases.
Kinetic energy is given by the equation:
You’ll notice that as v approaches c, kinetic energy approaches infinity. That means it
would take an infinite amount of energy to accelerate a massive object to the speed of
light. That’s why physicists doubt that anything will ever be able to travel faster than the
speed of light.