The range R of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its original altitude. (In other words, the range is the distance between the launch point and the impact point on flat ground.) A projectile is launched at t = 0 with initial speed vi at an angle θ above the horizontal.
(a) Find the time t at which the projectile returns to its original altitude.
(b) Show that the range is

(c) What value of q gives the maximum range? What is this maximum range?

v, sin 2