Relativistic momentum and relativistic energy

Example: 1
(a) An observer on Earth sees a spaceship at an altitude of 4350 km moving
downward toward Earth with a speed of 0.970c. What is the distance
from the spaceship to Earth as measured by the spaceship’s captain?
(b) After firing his engines, the captain measures her ship’s altitude as 267
km, while the observer on Earth measures it to be 625 km. What is the
speed of the spaceship at this instant?

7.8 Relativistic momentum and relativistic energy
Properly describing the motion of particles within the framework of
special relativity requires generalizing Newton’s laws of motion and the
definitions of momentum and energy. These generalized definitions reduce to
the classical (nonrelativistic) definitions when u is much less than c.


We have seen that the definition of momentum required generalization to
make it compatible with the principle of relativity. Likewise, the definition of
kinetic energy requires modification in relativistic mechanics. Einstein found
that the correct expression for the kinetic energy of an object is




Example: 2
An electron moves with a speed u = 0.850c. Find its total energy and kinetic
energy in mega electron volts (MeV), and compare the latter to the classical
kinetic energy (106 eV= 1 MeV).