Calculate the height above ground that a certain mass on Earth would need to be lifted in order to account for a certain gravitational potential energy change.

Example question:

On Earth a mass of 15 kg gains 350 J of gravitational potential energy. How high was it lifted?

Given:

gravitational acceleration: g = 9.8 m/s/s (on Earth)

mass: m = 15 kg

gravitational potential energy: Ug = 350 J

Starting formula

Algebra: divide each side by g

Algebra: g's cancel on right

Algebra: divide each side by m

Algebra: m's cancel on right

Algebra: swap right and left

Plug in values with units

Math: (350)/((9.8)(15)) = 2.380....

Final result with significant figures and unit