An astronaut is out in space with an extremely precise timing device measuring the speed of various fast‑moving objects. A laser gun is mounted on a spaceship and aimed backward. As the spaceship flies away from the astronaut at a speed of 100100 million m/s, the laser shines a beam of light toward him. Determine the speed that would be measured in each of the cases listed.

In a game of pool, ball a is moving with a velocity v0 of magnitude v0 = 15 ft/s when it strikes balls b and c, which are at rest and aligned as shown. knowing that after the collision the three balls move in the directions indicated and assuming frictionless surfaces and perfectly elastic impact (that is, conservation of energy), determine the magnitudes of the velocities va, vb, and vc.