At the Earth's surface, a projectile is launched straight up at a speed of 8.4 km/s. To what height will it rise? Ignore air resistance and the rotation of the Earth.

Answer 1

Set the initial kinetic energy equal to the potential energy change at the highest elevation, and solve for that elevation.

(1/2)mV^2 = GMm/R - GMm/(R + h)

Solve for the height h. m cancels out
M is the mass of the earth, G is the universal gravity constant and R is the earth's radius.