How does one calculate vertical jump height power requirements?

 

For instance, how many kN of force would be necessary to jump two meters vertically? By extension, I want to be able to determine how high would one be propelled if they were launched by 30, 40, 50, and 60 kN of force.

You need to figure out how long the force is applied. For example if a person with a mass of 100kg is subjected to an upwards force of 30kN the acceleration is 300m/s^3. Without gravity or air resistance this person would thus reach a respectable speed of 30m/s in 0.1 seconds. Someone else probably remembers how you calculate the apex point when air resitance and acceleration downwards (9.81m/s^3) are known.

Well firstly you need a force greater than that of gravity to move upwards so greater than mg and then to work out how high you'd go as Gilded said you need to know how long that force is applied for so you can then work out a maximum velocity from the acceleration using F=ma (assuming the mass is not changing), from the max velocity you can then work out with an acceleration due to gravity (9.81m/s/s) the height at which the velocity is 0 which will be the max height.

 

Adding in air resistance is harder as it's velocity depended.