Two astronauts, each having a mass of 74.0 kg, are connected by a d = 9.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 4.50 m/s. (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. kg · m2/s (b) Calculate the rotational energy of the system. kJ (c) By pulling on the rope, one of the astronauts shortens the distance between them to 5.00 m. What is the new angular momentum of the system? kg · m2/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? kJ (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope?

In the nineteenth century, gregor mendel first determined some basic rules of genetics that have been observed throughout all types of life. no observations have disproved these basic rules of genetics. charles darwin developed the idea of biological evolution around the same time, but he was unaware of mendel’s discoveries in genetics. over a century later, darwin’s idea of evolution was modified in order to incorporate mendel’s rules of genetics along with the other evidence that darwin had used. what is most likely the relationship between mendel’s rules of genetics and darwin’s idea of biological evolution? a.)mendel’s genetics states laws that are now part of the theory of biological evolution. b.)biological evolution states laws that are part of mendel’s theory of genetics. c.)mendel’s genetics replaced darwin’s entire concept of biological evolution. d.)biological evolution is a law that explains why all genetics exist.