If a projectile is fired with an initial velocity of vo meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after seconds is given by the parametric equations x = (vo cos α) t y = (vo sin α) t – ½ gt2 where is the acceleration due to gravity (9.8 m/s2).
(a) If a gun is fired with α = 30o and vo = 500 m/s, when will the bullet hit the ground? How far from the gun will it hit the ground? What is the maximum height reached by the bullet?
(b) Use a graphing device to check your answers to part (a). Then graph the path of the projectile for several other values of the angle α to see where it hits the ground. Summarize your findings.
(c) Show that the path is parabolic by eliminating the parameter.