Eliminate t from the two equations
x = vtcos��(theta) �; y = vtsin(theta)-(gt^2/2)
;
and obtain a relationship between x and y (assume that v; g and � are constants).
read the "trajectory" article at wikipedia.
To eliminate t from the two equations, we can solve one equation for t and substitute the value into the other equation. Let's start with the first equation:
x = v * t * cos(theta)
To isolate t, we divide both sides of the equation by v * cos(theta):
x / (v * cos(theta)) = t
Now we have t in terms of x, v, and theta.
Next, we substitute this value of t into the second equation:
y = v * t * sin(theta) - (g * t^2 / 2)
Replacing t with x / (v * cos(theta)) in the equation:
y = v * (x / (v * cos(theta))) * sin(theta) - (g * (x / (v * cos(theta))))^2 / 2
Simplifying further:
y = x * tan(theta) - (g * x^2) / (2 * v^2 * cos^2(theta))
Therefore, the relationship between x and y is given by:
y = x * tan(theta) - (g * x^2) / (2 * v^2 * cos^2(theta))