Question

Two particles move toward each other with velocities `v_1=0.50c` and `v_2=0.75c` relative to a laboratory frame of reference. Find:
(a) the approach velocity of the particles in the laboratory frame of reference,
(b) their relative velocity.

Answer 1

(a) By definition the velocity of approach is
`v_(approach)=(dx_1)/(dt)-(dx_2)/(dt)=v_1-(-v_2)=v_1+v_2`
in the reference frame K.
(b) The relative velocity is obtained by the transformation law
`v_r=(v_1-(-v_2))/(1-(v_1(-v_2))/(c^2))=(v_1+v_2)/(1+(v_1v_2)/(c^2))`