MATLAB

Problem 16: From the projectile problems that you have done as part of Physics & Dynamics courses, you know that the distance a projectile travels when fired at an angle 0 is a function of time and can be divided into horizontal and vertical distances according to the formulas: horizontal(t) =t V, cos0 vertical(t) = t Vo sino where: horizontal distance traveled in the horizontal direction vertical distance traveled in the vertical direction initial velocity (in m/s) acceleration due to gravity (9.8 m/s) time (in seconds) Vo A projectile is fired from the edge of a 150-m high cliff with an initial velocity of vo m/s at an angle of 0 with the horizontal, as shown in the figure: 150 m Part (a) Suppose the above projectile is fired at an initial velocity (vo1) of 180 m/s and a launch angle of 01 = 30 degrees (Case 1). Use MATLAB to plot the Vertical distance (on y-axis) vs. Horizontal distance (on x-axis) for time t = 25 seconds. Part (b) Now suppose we vary the launch angle 0 and the initial velocities as per the following two cases (Case 2 corresponding to 02 & vo2, and Case 3 corresponding to 03 & vo3): Launch Angle 0 (in degrees): 02=20, 03= 40 Initial Velocities (in m/s): V02= 160, v03= 150 Use MATLAB to plot vertical distance (on y-axis) versus horizontal distance (on x-axis) for all three cases (Cases 1, 2 and 3) on the same plot (include proper plot title, axis labels and plot legends). Part (c) The plots obtained in Part (b) show the projectile motion for negative values of the vertical distance (the second equation above). These negative values do not make sense physically since the projectile has already hit the ground. Modify the vertical and horizontal distance vectors and plot the graph again (vertical distance versus horizontal distance for all three cases), so that the plot shows only the positive values of the vertical distance travelled by the projectile. Part (d) Using the modified horizontal distance vector found in part (c), write MATLAB code to find the distance travelled by the projectile horizontally until it hits the ground (for all three cases). For which of the three cases is the horizontal distance traveled by the projectile maximum? Part (e) Using the modified vertical distance vector found in part (c), write MATLAB code to find the values of the maximum elevation reached by the projectile (for all three cases). For which of the three cases is the highest elevation reached by the projectile maximum