The path of a projectile fired from level ground with a speed of v0 feet per second at an angle a with the ground is given by the parametric equations x (v0 cos )t, y 16t2 (v0 sin )t a Show that the path is a parabola (b) Find the time of flight (c) Show that the range (horizontal distance traveled) is (v20 32) sin 2a (d) For a given vo, what value of a gives the largest possible range

Question: The path of a projectile fired from level ground with a speed of v0 feet per second at an angle a with the ground is

The path of a projectile fired from level ground with a speed of v0 feet per second at an angle a with the ground is given by the parametric equations
x = (v0 cos α)t, y = - 16t2 + (v0 sin α)t
a. Show that the path is a parabola.
(b) Find the time of flight.
(c) Show that the range (horizontal distance traveled) is (v20/32) sin 2a.
(d) For a given vo, what value of a gives the largest possible range?

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