Consider as a system the sun with jupiter in a circular orbit around it. find the magnitude of the change in the velocity of the sun relative to the center of mass of the system during the time jupiter completes half an orbit. assume the mass of the sun is 5.68 x 10^29 kg, the mass of jupiter is 1.90 x 10^27 kg, its period is 3.74 x 10^8 s, and the radius of its orbit is 7.78 x 10^11 m. ignore the influence of other celestial objects.

Animals respond in various ways to stimuli detected through their senses. some of these responses are stimulated by the presence of danger. which of these animal responses is the best example of a response to an immediate threat? a) a rooster crows every morning at the first sign of light. b) as something approaches an octopus, it shoots a cloud of ink. c) from late fall until spring, bears hibernate to preserve energy. reactivate d) a dog is getting hot in the sunlight, so he moves to a shaded area.

The boy of mass 30 kg is at r1= 2 meters from the fulcrum. of the girl is 45 kg, at what r2 must she sit so that they are balanced ?

Engineers find a new metal that is stronger than steel but much lighter. this material is also significantly cheaper than what is currently used for most aircraft, available in large quantities, and easy to manufacture. the engineers are excited because this new material will lower the costs of buying and operating airplanes for companies. what is probably the best step for the engineers to make next?