Why do this problem?
This problem provides an interesting application of conservation of kinetic and potential energy, and introduces students to ideas of non-constant gravity. The ideas raised, including the extrapolation to black holes, will be very interesting to most students and may inspire the students to look further into the ideas raised outside of the classroom.
Students may initially attempt to conserve energy using the approximation that gravity is a constant 9.8. They should be encouraged to see why this approach would be invalid. The activity best works as a hands-on task. One of the hurdles is accurate computation and students should be encouraged to provide numerical checks.
- What assumptions will you need to make in this calculation?
- How significantly do you think that this will affect the result?
The energies required to propel an object to the escape velocity are enormous. As an extension, students could try to calculate these energies for everyday objects or something of around the size of a UFO.
For an easier introduction to these ideas, try the problem Cannon Balls