Compute all parts of given problem:

Problem: A starship moving away from Earth with a speed of 0.81c launches a shuttle craft in the reverse direction, that is, toward Earth.

Part I: If the speed of the shuttle craft relative to the starship is 0.40c, and its proper length is 19 m, how long is the shuttle craft as measured by an observer on Earth?

Part II: If the shuttle craft had been launched in the forward direction instead, would its length as measured by an observer on Earth be greater than, less than, or the same as the length found in part (a)?

Part III: Calculate the length for the case described in part (b).

Show all work, use additional paper if necessary.