The bow stores elastic energy roughly E = 1/2 F_draw d k (draw length d = 0.7 m, force-draw filling factor k = 0.65) and hands 80% of it to the arrow: v0 = sqrt(2 eta E / m). A 200 N recurve with a 25 g arrow gives about 54 m/s.

In flight the arrow obeys dv/dt = -g - (1/2) rho Cd A |v_rel| v_rel / m with rho = 1.2 kg/m3 and a frontal area of 0.5 cm2. Without drag the path is the parabola with range x = v cos(th) (v sin(th) + sqrt(v^2 sin^2(th) + 2 g y0)) / g (release height y0 = 1.6 m); drag shortens it, more for light arrows. Wind enters through the relative velocity.

Simplifications: the arrow is a point mass with constant Cd (no spin, no fletching dynamics, no paradox flex) and constant efficiency. The target is a plain sport target; this is a sports-physics model only.