Show that the variation of gravity with height can be accounted for approximately by the following potential energy function: V-max(1-²) = mgz in which re is the radius of the Earth. Find the force given by the above potential function. From this find the component differential equations of motion of a projectile under such a force. If the vertical component of the initial velocity is toz, how high does the projectile go?

Show that the variation of gravity with height can be accounted for approximately by the following potential energy function: V-max(1-²) = mgz in which re is the radius of the Earth. Find the force given by the above potential function. From this find the component differential equations of motion of a projectile under such a force. If the vertical component of the initial velocity is toz, how high does the projectile go?