# Parabolic Shot/es

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ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.

## Mathematical function to follow

We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon.

The mathematical equations that govern the trajectory are:

$\displaystyle X(t)=V_{0x}\cdot t+X_0$

$\displaystyle Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0$

where:

$\displaystyle t$ = the current time for the mathematical equation.

$\displaystyle X$ = the 'x' coordinate of the bullet at a time 't'

$\displaystyle Y$ = the 'y' coordinate of the bullet at a time 't'

$\displaystyle X_0$ = the 'x' position of the bullet at time t = 0

$\displaystyle Y_0$ = the 'y' position of the bullet at time t = 0

$\displaystyle V_{0x}$ = the 'x' component of the velocity when shot (t = 0)

$\displaystyle V_{0y}$ = the 'y' component of the velocity when shot (t = 0)

$\displaystyle G$ = the gravity's acceleration.

You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy:

$\displaystyle V_{0x} = V_0 \cdot \cos \varphi$

$\displaystyle V_{0y} = V_0 \cdot \sin \varphi$

where:

$\displaystyle V_0$ = the velocity when shot (t = 0)

$\displaystyle \varphi$ = the cannon shooting angle with the horizontal.

See this Wikipedia article if you need more information regarding the maths equations of a parabolic shot.

 Language: English • español