Question

how can we maximize a range of projectile

Answer 1

to maximize  the range with respect to the firing angle θ we differentiate R with respect to θ and set this equal to 0. g 2 ∙ cos 2θ ( ) ∙ 0 therefore 2θ π 2 from which we obtain θ π 4 or 45 degrees. Suppose now we fire the projectileup a ramp which makes an angle α with respect to the horizontal.