Final answer:
To find the height at which the rocket is moving at a speed of 2 m/s, we can use the principle of conservation of energy. The rocket's potential energy will be equal to its remaining kinetic energy at that height. By setting up an equation and solving for height, we find that the rocket is approximately 0.204 meters off the ground when it is moving at a speed of 2 m/s.
Step-by-step explanation:
To find the height at which the rocket is moving at a speed of 2 m/s, we can use the principle of conservation of energy. Total energy is given by the sum of kinetic energy and potential energy. At the beginning, the rocket has an initial kinetic energy of (1/2) * mass * velocity^2, which can be calculated as (1/2) * 10 kg * (53 m/s)^2. As the rocket rises, its potential energy increases while its kinetic energy decreases. At the desired height, the potential energy will be equal to the remaining kinetic energy, so we can set up the equation (1/2) * 10 kg * (2 m/s)^2 = mass * gravity * height to find the height.
Simplifying this equation gives us (1/2) * 10 kg * (2 m/s)^2 = 10 kg * 9.8 m/s² * height. Solving for height, we find height = (1/2) * (2 m/s)^2 / (9.8 m/s²) = 0.204 m. Therefore, the rocket is moving at a speed of 2 m/s when it is approximately 0.204 meters off the ground.