Question

two cars are moving with same velocity c/2 .these are perpendicular to each other .find relative velocity.

Answer 1

As Lorenz transformation is $u=\frac{\sqrt{(u'^2+v^2+2vu'\cos\theta'-(\frac{vu'\sin\theta'}{c})^2}}{1+\frac{vu'\cos\theta'}{c^2}}$ (J.D.Jackson,Classical Electrodynamics, N.Y-London,1962)

We have $u'=v=c/2, \theta'=\pi/2$ then $u=c\sqrt{7/16}$