What would become of the earth's orbit (which you may consider to be a circle) if half of the sun's mass were suddenly to disappear? would the earth remain bound to the sun? [hints: consider what happens to the earth's ke and pe at the moment of the great disappearance. the virial theorem for the circular orbit (problem 4.41) with this one.] treat the sun (or what remains of it) as fixed.

Afisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. it takes a time of 2.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.670 m . the fisherman sees that the wave crests are spaced a horizontal distance of 5.80 m apart. (a) how much is the wavelength? (b) find the period of the wave. (c) how fast are the waves traveling? (d) what is the amplitude a of each wave?