A soccer ball is kicked straight upwards with an initial vertical speed of 8.0 ms8.0\,\dfrac{\text m}{\text s} 8.0 s m 8, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction . We can ignore air resistance. How long does it take the ball to have a downwards speed of 4.0 ms4.0\,\dfrac{\text m}{\text s} 4.0 s m 4, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction ?

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?