Relative Velocity

The particles are moving with velocities

0.8%20%5C%2Cc

and

-0.4%5C%2C%20c

in the laboratory frame, say

S%5E%7B%5Cprime%7D

frame. Let

S

be a reference frame in which the particle with velocity

-0.4%5C%2C%20c

is at rest. Then, the velocity of

S%5E%7B%5Cprime%7D

(laboratory) relative to

S

v%3D0.4%5C%2C%20c

. Therefore, the particle which in

S%5E%7B%5Cprime%7D

has velocity

u%5E%7B%5Cprime%7D%3D%2B0.8%5C%2C%20c

has a velocity in S given by

u%20%3D%5Cfrac%7Bu%5E%7B%5Cprime%7D%2Bv%7D%7B1%2B%5Cfrac%7Bu%5E%7B%5Cprime%7D%20v%7D%7Bc%5E%7B2%7D%7D%7D

%3D%5Cfrac%7B0.8%20c%2B0.4%20c%7D%7B1%2B%5Cfrac%7B(0.8%20c)(0.4%20c)%7D%7Bc%5E%7B2%7D%7D%7D

%3D%5Cfrac%7B1.2%20c%7D%7B1%2B0.32%7D%3D0.9%20c

Chapter Questions
1 MCQs