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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, s

_{x}= u

_{x}t

in vertical, s

_{y}= u

_{y}t + 1/2 gt

^{2}

KE = 1/2 mv

^{2}

PE = mgh

## The Attempt at a Solution

L = KE - PE

= 1/2 m ( v

_{x}

^{2}+ v

_{y}

^{2}) - 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.