contine the other three d,e,f Two astronauts, each having a mass of 89.0 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 5.90 m/s. Treating the astronauts as particles, calculate each of the following.Illustration Description:- Two astronauts are shown connected by a rope with a length \(d = 10.0\) meters.- The center of gravity (CG) is marked as the midpoint of the rope.- Arrows indicate the circular motion of the astronauts around the CG.(a) The magnitude of the angular momentum of the system:\[ \text{5251 kg} \cdot \text{m}^2/\text{s} \](b) The rotational energy of the system:\[ \text{3.09 kJ} \]By pulling on the rope, the astronauts shorten the distance between them to 5.00 m.(c) What is the new angular momentum of the system?\[ \text{5251 kg} \cdot \text{m}^2/\text{s} \](d) What are their new speeds?\[ \text{ m/s} \](e) What is the new rotational energy of the system?\[ \text{ kJ} \](f) How much work is done by the astronauts in shortening the rope?\[ \text{ kJ} \]

d)Write the equation for the conservation of the angular momentum and substitute the corresponding…

Two astronauts, each having a mass of 89.0 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 5.90 m/s. Treating the astronauts as particles, calculate each of the following. CG d (a) the magnitude of the angular momentum of the system 5251 kg. m²/s (b) the rotational energy of the system 3.09 kJ (d) What are their new speeds? m/s By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? 5251 kg. m²/s (e) What is the new rotational energy of the system? KJ (f) How much work is done by the astronauts in shortening the rope? KJ