Five astronauts (A - E) are watching a star collapse to form a black hole. Which of the flight plans require that the astronaut travel faster than light?

The pilot of a space ship shines a laser pointer from the back of the ship to the front. The laser travels at the speed of light 300,000 km/s with respect to the ship, which is itself moving at 100,000 km/s. What will be the speed of the laser beam according to an observer at rest  outside the ship? Express your answer in km/s

You pitch a baseball to your friend from the back of a pick-up truck. You know that you pitch at 40 m/s, but your friend reports that he caught the ball going 10 m/s. What is the speed of the truck? (Use Galilean/Newtonian relativity.

For an astronaut traveling to a star 10 lightyears away at v=0.99c  and returning, spending negligible amount of time at the destination, describe the journey as the astronaut would observe it. In particular, describe what the astronaut would observe as happening on Earth during the journey

The special theory of relativity is "special" because it deals only with a certain type of reference frames, inertial reference frames.  What are inertial reference frames?

While on board a starship, you intercept signals from four shuttle craft that are moving either directly toward or directly away from you.The signals have the same proper frequency f0.The speed and direction (both relative to you) of the shuttle craft are (a) 0.3c toward, (b) 0.6c toward, (c) 0.3c away, and (d) 0.6c away. Rank the shuttle craft according to the frequency you receive, greatest first.

A particle maintains a circular orbit around a black hole of mass 10 Solar masses at a distance equal to 2 Schwarzschild radii. Calculate the orbital velocity of the particle and express the answer in units of the speed of light.

What will be the Schwarzschild radius of Earth?