Maybe provide some explanation

Let O=(l,H), A=(0,0), B=(l,0). System of coordinates: OX=AO, OY =  BO rotate on teta (teta=arctan(H/l)).
Then:

vx(t) = (v+gt)*sin(teta)
vy(t) = (v-gt)*cos(teta)

x(t) = V*sin(teta)+g*sin(teta)*(t^2)/2
y(t) = V*cos(teta)-g*cos(teta)*(t^2)/2

First point: (l, H) => x=0, y=0
Second point: y(t)=0 <=> t=2*v/g
              x(2*v/g) = 4*(V^2)*sin(teta)/g = d = 8 * h * sin(teta) (mg(H+h)=mgH+m*(V^2)/2)
              x = d, y = 0

Distance between First point and Second point = d
Distance between Second point and Third point = 2*d
...
Distance between i point and i+1 point = i*d

If n = answer => d+2d+3d+...+(n-1)d<=sqrt(H^2 + l^2)
                 d+2d+3d+...+(n-1)d+nd>sqrt(H^2 + l^2)

Edited by author 05.08.2018 12:52