1. The problem statement, all variables and given/known data Find the differential equations of motion of a projectile in a uniform gravitational field without air resistance. 2. Relevant equations For the motion of a projectile, in horizontal, sx = ux t in vertical, sy = uy t + 1/2 gt2 KE = 1/2 mv2 PE = mgh 3. The attempt at a solution L = KE - PE = 1/2 m ( vx2 + vy2 ) - mgy Then find their partial differentiation in terms of x, x_dot, y and y_dot. However, the answer claims that there is z-direction motion. Why z direction takes into the case? Thankyou.