If a projectile is fired with an initial velocity at an angle of inclination from the horizontal, then its trajectory, neglecting air resistance, is the parabola (a) Suppose the projectile is fired...

If a projectile is fired with an initial velocity at an angle of inclination from the horizontal, then its trajectory, neglecting air resistance, is the parabola

(a) Suppose the projectile is fired from the base of a plane that is inclined at an angle a, a > 0, from the horizontal, as shown in the figure. Show that the range of the projectile, measured up the slope, is given by


(b) Determine so that R is a maximum.
(c) Suppose the plane is at an angle a below the horizontal.
Determine the range R in this case, and determine the angle at which the projectile should be fired to maximize R.