What is Escape Velocity? Derivation of Escape Velocity Equation // HSC Physics

This video in on the concept of escape velocity, including derivation of an equation for escape velocity using the law of conservation of energy

📚Syllabus
• Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but not limited to:
– the concept of escape velocity 𝑣_esc=√(2𝐺𝑀/𝑟)
– total potential energy of a planet or satellite in its orbit U=−𝐺𝑀𝑚/𝑟
– total energy of a planet or satellite in its orbit U+K=−𝐺𝑀𝑚/2𝑟
– energy changes that occur when satellites move between orbits
– Kepler’s Laws of Planetary Motion

What is the definition of escape velocity? How to derive equation for escape velocity?

[tairamehring]

If there is an object not on the surface of the earth, but instead at some radius further away would the overall radius also apply into the formula? So like an object in circular motion around earth will have a radius from the centre of the earth to the surface + altitude

[fizixx]

Can this equation be derived using kinematic equations?