You are asked to design a catapult that can throw stones, one stone at a time, accurately into a container. The trajectory of a stone thrown by the catapult can be modelled as g y=(tan)x- 2V cos 0 x + yo Here, 0, is the initial angle of interest, the horizontal distance, x=am, gravity, g = 9.81 m/s, the initial velocity, V = 30 m/s, and the initial height (elevation), yo = 5 m. Here, a = 2 sum of your student ID. Vo For example, for student ID = 123 456 789, a = 2(1+2+3+4+5+6+7+8+9)=90 Yoo 00 Use the Newton-Raphson method to solve for 0, start with an initial guess of 45. X Calculate until the approximate error is less than 0.001 or the number of iteration is no more than 50. If it takes less than 3 iterations to converge, change the initial guess so that it takes at least 3 iterations before convergence.