A mortar gun with a maximum range of 40 m on level ground

Question

A mortar gun, with a maximum range of 40 m on level ground, is placed on the edge of a vertical cliff of height 20 m overlooking a horizontal plain. Show that the horizontal range R of the mortar gun is given by

R = 40{sin α + (1 + sin² α)^1/2} cos α,

where α is the angle of elevation of the mortar above the horizontal.

[Take g = 10 m s^-2.]

Evaluate R (to he nearest metre) when α = 45° and 35° and confirm that α = 45° does not yield the maximum range.