Compute the trajectory of a 155 mm artillery shell launched with a muzzle velocity of 700mlsec at an angle of 45 degree

Parameters : r(0) = (x(0),y(0)) = (0,0) |V(0)| = 700 m/sec (mach 2) V(0) = (Vx(0),Vy(0)) = (495, 495) m/sec m = 50 kg g = 9.8 m/sec2 theta (0) = 45 drag coefficient cD = 0.275 cross-section A = 0.0189 m2 rho (air density) = 1.225 kg/m3 deltaT = 1.0 sec (time increment for calculations)

Force law (approximate) :

Fx = -(Cd A rho |V|2 / 2) cos(theta) = -0.0032 cos(theta) (Vx2 + Vy2) Fy = -mg - (Cd A rho |V|2 / 2) sin(theta) = -490 - 0.0032 sin(theta) (Vx2 + Vy2)

Compute the trajectory of a 155 mm artillery shell launched with a muzzle velocity of 700 m/sec at angle of 45

Algorithm (Verlet) t=0

ax(0) = Fx(0)/m // initialize force and acceleration components ay(0) = Fy(0)/m

Do until y(t) < 0 : // recompute position x(t+deltaT) = x(t) + Vx(t) deltaT + 0.5 ax(t) deltaT2 y(t+deltaT) = y(t) + Vy(t) deltaT + 0.5 ay(t) deltaT2 // recompute velocity Vx(t+deltaT) = Vx(t) + ax(t) deltaT Vy(t+deltaT) = Vy(t) + ay(t) deltaT // recompute angle with respect to horizontal theta(t+deltaT) = arctan(Vy(t+deltaT)/Vx(t+deltaT)) // recompute force and acceleration components ax(t+deltaT) = Fx(t+deltaT)/m ay(t+deltaT) = Fy(t+deltaT)/m t = t + deltaT // update current time

A) Implement in Python the Verlet algorithm to compute the trajectory of the 155mm shell, using all the parameters shown below. Your implementation must produce a plot of altitude(Y) versus horizontal position(X), and report the FINAL position(X,Y) produced by the simulation.

B) Answer this question-how do you know that your computation is at all reliable? Assuming the physics(forcelaw)is exactly correct, how can you determine if the algorithm itself is producing a reliable result?What parameter of the computation might make an impact. Can you make an attempt to evaluate the reliability of the computation?

Answer should contain:

1. File on Python code that was used to solve that problem

2. A brief report on what you did, what youre trying to solve, sample input and output