(1) What is the rocket's escape velocity? (Note the mass of the rocket is irrelevant- why?)
At infinitely far away with 0 velocity, the rocket will have 0 potential energy (by designation) and 0 kinetic energy. As it is launched, however, it has both kinetic and potential energy. The only force acting is gravity, a conservative force. Therefore, mechanical energy is conserved, and the following equation must hold:
where m is the mass of the rocket, is escape velocity, M is the mass of the Earth, and R is the radius of the Earth. The mass of the rocket can be divided out of the equation (hence it is irrelevant to the problem). Solving for yields
