Two futuristic rockets are on a collision course. Rocket 1 is moving with speed 0.41c relative to Earth and rocket 2 is moving with speed 0.644c relative to Earth. They are initially separated by a distance of 2.53 × 1012m as measured by Liz, an observer on Earth. Both rockets are 57.9m in length as measured by Liz. (a) What is the proper length of rocket 1? (b) What is the proper length of rocket 2? (c) What is the length of rocket 1 as measured by an observer in the other rocket? (d) According to rocket 2, how long before they collide? (e) According to Liz, how long before the rockets collide?