Solve the given problems:
Problem I: A spacecraft passes earth moving eastward at the speed of a particle whose kinetic energy is 13.5 times its rest energy. Find the speed of the particle?
Problem II: A right triangle, on the floor of the spaceship, has its height (16.0 m) in the north-south direction while its base (12.0 m) is in the east-west direction according to the occupants of the ship. What are the dimensions of the triangle according to the earthbound observer? Find the hypotenuse of the triangle according to this observer. Problem III: According to this earthbound observer, what is the half-life of a sample of smium-191 in the captain's laboratory, on the spacecraft if an osmium at rest has a half-life of 15.4 d?
Please provide steps, equations used in solution.