Final answer:
The student's question involves calculating the relative speed of Carl's spaceship from Bob's perspective, using the relativistic velocity addition formula, and understanding that Carl's speed relative to Earth is observed as 0.9c and remains constant from Earth's frame of reference.
Step-by-step explanation:
The question is about calculating relative velocities in special relativity, specifically when dealing with speeds that are a significant fraction of the speed of light (denoted as c). Given that Bob is on a spaceship moving at 0.8c toward Earth and Carl is on a spaceship moving at 0.9c toward Earth, we need to use the formula for relativistic addition of velocities to find the answers.
a) According to Bob, the velocity of Carl's spaceship relative to him can be calculated using the relativistic velocity addition formula: v = (v1 + v2) / (1 + (v1 * v2) / c2), where v1 is Bob's velocity relative to Earth (0.8c) and v2 is Carl's velocity relative to Earth (0.9c). Solving this equation would yield the relative speed of Carl to Bob.
b) The velocity of Carl relative to Earth is given as 0.9c, and it remains constant from Earth's frame of reference. Bob's observations about Carl's speed do not change Carl's speed relative to Earth.