(1) can have the maximum range without derivative. The ordinate of X point and origin is zero, and the X-axis coordinates of these two points can be regarded as two equations Y = KX-1/20 (1+k2) x2 = 0, so besides the origin, another solution is X = 20k/( 1+k 2).

(2) At the height of 3.2m, between the spans of the artillery trajectory, the artillery can adjust the angle to hit the flying object, so if the abscissa of the flying object is outside the span, it cannot hit. According to this method, the intersection of the trajectory and the straight line y=3.2 can be set as A and B, and the abscissa of the two points is x 1, x2. Then x 1, X2 is the two roots of the equation y = y = kx-1/20 (1+k2) x2 = 3.2. To fight, the equation about k: x 2 * k 2-20x * k+64+x 2 = 0 has a positive root. =0，x