python

In this lab exercise you will re-visit projectile motion (motion in 2-D), plotting the trajectory with a slightly different method. The vector equations of motion governing the projectile are:(a - acceleration, v(t) - velocity; s - displacement, t - time): a = vo taxt (1) ' = s + v *t+d *t? (2) 2 + *** = The motion resolved into components is: x-component y-component vx = Vo * cos 0 + ax *t Vy Vo * sin 0 + Qy *t 1 x = xo + vo * cos 6 *t + (1/2) * Az *t y = yo + vo * sin 0 *t + The Method: *t2 Use numpy for the following exercise. To use numpy, first: import numpy as np import matpoltlib.pyplot as plt Now any numpy functions can be used, for example: np.cos(x*np.pi). numpy has its own library of functions. In the pro am use the functions from the numpy module. = (a) Choose a time interval At (a value in the range 0.01 to 0.05) and define the initial values of x, y, Vx, Vy, t. Start the projectile off at (200,0) with a specified initial velocity and angle. (b) Choose N - the maximum number of intervals (this gives the max. time : tmar N * At for the numerical solution). So at the kth time-step: tk k * At. Experiment with various values for N and At, to find a suitable plot for the trajectory ( as an estimate tmax ~ 2 * vo/g). (c) Note that acceleration is a constant and only acts in the y direction (i.e. = 0 & ay = -9) (d) Start by setting the current position to the initial position x = 200, y = 0; with current velocity components to the initial velocity components Vx = Vox, Vy ax = Voy. (e) Store the initial values of x, yt in numpy arrays.. Also store vox and voy in arrays. (see the previous lab for numpy arrays). -- (f) Next, iterate (loop) over the next 4 steps, repeating the steps while n<>