# What equations would you use for parabolic motion equations such as for horizontal motion, and for vertical motion?

garthman99 | Certified Educator

All of the equations used in projectile motion are based on the three basic kinematic equations

v = u + at

v^2 = u^2 + 2ax

x  = ut + (1/2)at^2

in these equations v represents final velocity, u represents initial velocity, a represents acceleration , x represents displacement and t represents time.

So if we apply these equations to the vertical motion we get

Initial vertical velocity = V sin theta

v(y) = v sin theta - gt    where v(t) is the vertical velocity at time t and v is the velocity

of projection. In this case the acceleration is that due

to gravity and is considered negative.

V^2 =( V sin theta)^2 - 2gy

y =  ( V sin theta)t - (1/2)gt^2      where y is vertical displacement

Since gravity does not act horizontally we have for the horizontal motion

Initial Horizontal velocity = V cos theta

V(x)= V cos theta       ( the horizontal velocity never changes )

x  =  ( V cos theta)t