The parametric equations for the motion of a projectile
$$ x = (v_0 \cos(\theta))~t$$
$$y = h+ (v_0 \sin(\theta))~t-16t^2$$
can be rewritten in rectangular coordinates as :
$$ y = \frac{- x^2 16 \sec^2(\theta)}{v_0^2}+ \tan(\theta)~x+h $$
The path of a projectile is given by the rectangular equation$y = 6 + x − 0.08x^2$.
(a) Find the values of $h,~ v_0,$ and $\theta$. Then write a set of parametric equations that model the path. (Use the given formulas to write the equations. Enter your answers as a comma-separated list of equations.)
I'm not sure how to do a), but I already graphed it and found the max height to $9.13 $ and the range to be $16.93 $ feet.
$\endgroup$1 Answer
$\begingroup$I think you made a slight mistake in either simplification or typesetting. You should get $$y=-\frac{16\sec^2\theta x^2}{v_0^2}+\tan \theta x +h$$
Now it should be simple to match each coefficient. The constant term, $h=6$. The coefficient of $x$ is $\tan \theta=1$. The coefficient of $x^2$ is $-16\sec^2\theta/v_0^2 = -0.08$. That should give you $h, v_0, \theta$.
$\endgroup$ 5
