Chapter 10.1, Problem 46E

If a projectile is fired with an initial velocity of v₀ meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations

$x=\left(v_0\cos \alpha \right)ty=\left(v_0\sin \alpha \right)t-\frac{1}{2}g{t}^2$

where g is the acceleration due to gravity (9.8 m/s²).

(a) If a gun is fired with a = 30° and v₀ = 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.