# Projectile Motion

Projectile motion is the study of how an object moves through the air. A projectile motion problem can be thought of as a 2 dimensional problem with motion in the horizontal direction (x direction) and motion in the vertical direction (y direction).

For the horizontal direction the velocity would be constant.  This is represented by the equations below.

(Eq 1)  $X(t)=Vx_ot+X_o$

(Eq 2)  $Vx(t) = Vx_o$

On the other hand for the vertical direction there is a constant acceleration due to gravity. This means that the gravitational acceleration will need to be considered when deriving the equation of motion.  Refer to the equations below.

(Eq 3)  $Y(t)=\frac{1}{2}g_ct^2+Vy_ot+Y_o$

(Eq 4)  $V_y(t)=g_ct+Vy_o$

(Eq 5) $a_y(t) = g_c$

The gravitational constant (g) in SI units is 9.81 m/s^2, while for British-American units it would be 32.2 ft/s^2. Below is an image showing what the typical path a particle would take when subject to projectile motion.