Suppose you throw a ball with horizontal part of the velocity x'(0) = 20 m/s and vertical part of the velocity y'(0) = 10 m/s. assuming that the gravitational force is constant (g = 9.8 m/s2) and that air resistance is proportional to the square of the velocity we obtain z" =-kk' /(x)2 + (y')2 " =-9 - ky' (x)2 + (y')2 x(0) = 0, x'(0) = 20, y(0) = 0, y(0) = 10. assuming the air resistance constant k= 0.1 m-1 find (a) the maximum height the ball will attain (b) how far from you will the ball hit the ground. details: for solutions of all differential equations you need to use the classical runge-kutta method developed in class. in parts a and b above you need to use newton's method.