Two spaceships are approaching Earth in perpendicular paths as measured from an observer on Earth (see figure). One of the spaceships, the USS Enterprise, travels towards Earth with a speed of 0.5c. The other spaceship, the USS Excalibur, approaches Earth with a speed of 0.7c. Both speeds are measured by an observer on the planet. (20 points)
1. Write down the Lorentzian speed component transformations.
ii. Find the relative speed of the USS Excalibur as detected by the USS Enterprise with and without relativistic corrections.