10. An astronaut at rest in space has a mass of 84 kg and fires a thruster that expels 0.035kg of hot gas at 875m/s to the right. What is the velocity of the astronaut after firing the thruster? Type a response

To solve this problem, we can use the principle of conservation of momentum. The total momentum of the system before firing the thruster must be equal to the total momentum of the system after firing the thruster.Let's denote the velocity of the astronaut after firing the thruster as .The momentum of the hot gas expelled by the thruster is given by the product of its mass and velocity, which is .The momentum of the astronaut before firing the thruster is zero since he is at rest.The momentum of the astronaut after firing the thruster is given by the product of his mass and velocity, which is .Using the conservation of momentum, we can write the equation: Solving for , we get: Therefore, the velocity of the astronaut after firing the thruster is to the left.