Use the expression in Problem 57 to find
(a) The maximum range of a projectile with launch speed vi and
(b) The launch angle q at which the maximum range occurs.
In problem 57
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.

v, sin 2