Parabolic motion and catapults?

Question

Ok i need to know how to right a equation that will represent the parabolic motion of a catapult!!!! Or the parabolic motion of the projectile that comes out of a catapult

If your not quite sure about my project go here and read anything that talks about waterfountain project or projectile motion
http://www.abhs.k12.nm.us/classes/Math/Stacey/11th%20Grade/Staceys11thGrade.htm

Answer 1

This is simple if you break it down into components
of vertical and horizontal motion.

Vh=constant
Vv is subject to acceleration due to gravity g

Then with a little trig we can express Vv and Vh by using firing velocity and firing angle A
Vh=Vcos(A)
Vv=Vsin(A)

Range S
S=Vh t where
t - total time in flight

Time to reach its highest point we use
Vv=gt
t=Vv/g

However be careful this is the time it takes to travel from the tip of the catapult (or gun) to the highest point of the trajectory h.
then
h=0.5 g t^2



Have fun

Answer 2

let
v be the initial velocity of the catapult
θ be the angle that the catapult fires at
y0 be the initial height that the catapult fires from
then (neglecting air resistance)

y = y0 + [tanθ]x - [g/2v²cos²θ]x²

is the parabola in the xy plane
where y is the height of the projectile at a horizontal distance of x from the catapult's origin

this equation can be derived from the 2-Dimensional equations of kinematics
x = (vcosθ)t
&
y = y0 + (vsinθ)t - ½gt²

just rearrange x = (vcosθ)t to give t = x/(vcosθ)
then substitute this in the equation for y
which eliminates t
and gives the result above

.,.,..,.,..,.,.