Two astronauts, each having a mass of 94.5 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.20 m/s. Treating the astronauts as particles, calculate each of the following.(a) the magnitude of the angular momentum of the system
(b) the rotational energy of the system
By pulling on the rope, the astronauts shorten the distance betweenthem to 5.00 m.
(c) What is the new angular momentum of the system?
(d) What are their new speeds?
(e) What is the new rotational energy of the system
(f) How much work is done by the astronauts in shortening therope?

Jasmine is diving off a 3-meter springboard. her height in meters above the water when she is x meters horizontally from the end of the board is approximated by the equation h=-x^2+3x+3. what is the maximum height jasmine will reach on her dive?

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)

The mass of the sun is 1.99×1030kg and its distance to the earth is 1.50×1011m. what is the gravitational force of the sun on the earth?