The position as a function of time (x(t), y(t)) of a projectile fired with a speed of vo at an angle a is given by x(t) = v₁cosα t y(t) = vo sina.t- 1 2812 Ꮎ 1 where g = 9.81 m/s². The polar coordinates of the projectile at time t are (r(t), 0(t)), where r(t) = √x(t)²+y(t)² and tane = y(1) Consider the case where vo x(t) and 0 = 70°. Determine r(t) and 0(t) for t = 1, 6, 11, 31s. = 162 m/s

2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…