Galileo, in his two new sciences, states that "for elevations (angles of projection) which exceed or fall short of 45 degrees by equal amounts, the ranges are equal. prove it.

The astronauts on the space shuttle flights experienced an acceleration of 29 m/s2 (about 3 "g's") during lift-off. what upward force must the astronaut's seat apply to the astronaut in order to cause this acceleration? assume the astronaut's mass is 70 kg, and compute this force when the acceleration is near the earth's surface so their weight equals latex: mg m g .