Two heavy astronauts, each having a mass of 120 kg , are travelling in a closed spaceship moving at a speed of 15 km/s in outer space, far removed from all other material objects. The total mass of the spaceship and its contents, including the astronauts, is 660 kg . If the astronauts perform slimming exercises, thereby reducing their individual masses to 90 kg , with what velocity will the spaceship move?

Step-by-step solution

Since the spaceship is a closed system, the mass lost by the astronauts remains inside the spaceship in the form of sweat, exhaled gases, and other metabolic byproducts. The total mass of the spaceship and its contents remains constant at 660 kg . As there is no external force acting on the spaceship in outer space, the total linear momentum of the system is conserved. With both the total mass and the total momentum of the system remaining constant, the velocity of the spaceship remains unchanged. Therefore, the sp