If I throw a 500g bomb into space with a speed of 0.52c. Calculate the bombs relativistic momentum.?

Answer 1

Relativistic momentum is given by,
p = gamma * mass * velocity,
where gamma is itself a function,
gamma = 1 / sqrt (1 - v^2 / c^2)
where v is the velocity of the object and c s the speed of light in a vacuum.
* of course, by velocity, I am referring to the velocity measured by the observer who wished to calculate the object's momentum.

p = mv / sqrt (1 - (v/c)^2)
m = .5 kg
v = .52 c
c = 3 E8 m/s

p = (.5 kg) * (.52 * 3 E8 m/s) * gamma
p = (7.8 E7 kg m/s) * gamma,
where gamma = 1/sqrt (1 - .52^2) = 1.171

so, p = 7.8 E7 * 1.171 = 9.13 E7 kg m/s

The relativistic momentum of the object as measured by the observer is 9.13 * 10^7 kg m/s.