A projectile with a mass m moving in a 2-D plane (OXZ), with x in the horizontal direction and z in the vertical direction pointing upwards: 

1- Deduce that the potential energy of the projectile is given by: 

        L=1/2m(x˙²+z˙²)+mgz 

2- By using the Lagrangian method write the motion equations along x and z-directions. 

3- By using the Hamiltonian method write the motion equations along x and z-directions.