Eliminate t from the two equations

x = vtcos��(theta) �; y = vtsin(theta)􀀀-(gt^2/2)

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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))