Cadet Competition Written Practice Exam

What determines the escape velocity of a rocket?

1. The mass of the rocket

2. The mass and radius of the planet

3. The type of fuel used

4. The design of the rocket

The correct answer is: The mass and radius of the planet

The escape velocity of a rocket is primarily determined by the mass and radius of the planet from which it is launching. This is because escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. The formula for escape velocity is derived from the conservation of energy principles, which encompass gravitational potential energy and kinetic energy. It can be expressed as: \[ v = \sqrt{\frac{2GM}{r}} \] Where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( r \) is the radius of the planet from its center to the point of escape. Therefore, both the mass of the planet and its radius play critical roles in determining how strong the gravitational pull is and consequently the speed required to escape that gravitational influence. The other options, while relevant in specific ways to rocket performance and function, do not directly influence the escape velocity in the same fundamental way. The mass of the rocket affects how much thrust is needed to launch but doesn’t change the escape velocity itself, which is a characteristic of the planet. The type of fuel influences the thrust and efficiency of the rocket but is not a factor in calculating the escape