What is the mass of a 70kg man in a space rocket traveling at 0.8c from us as measured from Earth?
[Ans. 116.7 kg]
Given:
Rest Mass of man = m₀ = 70 kg
Speed of the rocket relative to the observer on earth = v = 0.8 c
To Find:
Relativistic mass = m = ?
Solution:
The formula for relativistic mass in the special theory of relativity is given by:
m = m₀√1-v2c2m₀√1−v2c2
by putting values
m = 70kg√1-(0.8c)2c270kg√1−(0.8c)2c2
m = 70kg√1-0.64c2c2
c² will be canceled so,
m = 70kg√1-0.64
m = 70kg√0.36
m = 70kg0.6
m = 115.667 kg -----------------Ans.
Thus, when a man in a rocket traveling in space at speed v = 0.8 c, the relativistic mass of the man is measured as 115.667 kg.
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