If a projectile is fired with an initial velocity of $V$ meters per second at an angle $A$ above the horizontal and air resistance is assumed to be negligible, then its position after $t$ seconds is given by the parametric equations $$x = (V\cos(A))t, \quad y = (V\sin(A))t-\frac{1}{2}gt^2,$$ where $g$ is the acceleration due to gravity ($9.8\;m/s^2$).

(a) If a gun is fired with $A=30^{\circ}$ and $V=500\;m/s,$ when (in seconds) will the bullet hit the ground?

Time $t =$ seconds

(b) Under the conditions of (a), how far (in meters) from the gun will it hit the ground?

Distance = meters

(c) Under the conditions of (a), what is the maximum height (in meters) reached by the bullet?

Maximum height = meters

(d) Show that the path of the bullet is parabolic by eliminating the parameter to find a Cartesian equation that describes the path. Your answer may depend on $V$, $A$, $x$, $y$, and $g$. If $g$ appears in your answer, leave it in - do NOT substitute in $g = 9.8$ in your answer!

$y =$