Relative Velocity

The relativistic factor

%5Cgamma

is given by the formula:

%5Cgamma%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%7D

Where: -

v%20%3D%205000%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

is the velocity of the spaceship, -

c%20%3D%203%20%5Ctimes%2010%5E8%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

is the speed of light. Substituting the values:

%5Cgamma%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B1%20-%20%5Cfrac%7B(5000)%5E2%7D%7B(3%20%5Ctimes%2010%5E8)%5E2%7D%7D%7D

%5Cgamma%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B1%20-%20%5Cfrac%7B25%20%5Ctimes%2010%5E6%7D%7B9%20%5Ctimes%2010%5E%7B16%7D%7D%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B1%20-%202.78%20%5Ctimes%2010%5E%7B-10%7D%7D%7D

%5Cgamma%20%5Capprox%201.0001

Thus, the relativistic factor

%5Cgamma

for the spaceship is approximately

1.0001

Chapter Questions
1 MCQs