# Solve Lagrange's Mechanics Homework on Projectiles in Gravity

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## Homework Statement

Find the differential equations of motion of a projectile in a uniform gravitational field without
air resistance.

## Homework 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

## 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.

However, the answer claims that there is z-direction motion.
Why z direction takes into the case?
if there is a general motion of projectile i.e. there are velocities in x,y,z directions at t=0 one can have equations of motion.
first one must choose the direction of gravitational field and a natural choice will be z.

if there is a general motion of projectile i.e. there are velocities in x,y,z directions at t=0 one can have equations of motion.
first one must choose the direction of gravitational field and a natural choice will be z.
Thanks I got the idea