Question

1 2 A projectile PA is launched from point A towards the east with an initial launch velocity ves and an initial launch angle of 8aA. The impact point of the projectile Pa is a point B in a valley with an ordinate, you, located below the elevation of point A. The launch from point A is instantaneously detected at point B, and a counter projectile Pa ts launched simultaneously towards the west to intercept the incoming projectile PA. Projectile Pn has a launch velocity Vos. What should be the launch angle Bas of projectile Ps in order to intercept projectile PA. Assume zero air resistance during flight. Assume point A is located at the origin of the right hand Cartesian coordinate system with x pointing in the east direction and y is the altitude. VoA-5S0 m/s ve"- 900 m/s aa = 40 yos =_3ooom deg. Answer the following questions based on the results of your MATLAB program: 1. Launch angle Gos in degrees of projectile Ps. 2. Distance in meters from point A to B 3. Time of flight in seconds from point A to point B of projectile PA 4. Maximum height in meters of projectile P 5. Maximum height in meters of projectile Ps. 6. Time at intercept in seconds from launch if there is an intercept. 7. Coordinates of intercept (Xe Ye) in meters between PA and Pn Derive all the relevant equations necessary to determine intercept between the two projectiles. Make a diagram to show the trajectories and indicate the variables that will be used in the development of the equations. DO NOT USE NUMBERS WHILE DERIVING THE EQUATIONS. Using MATLAB write a script file to do the following: 1. Calculate the trajectories of PA and Ps 2. Answer to questions 1-7 listed above. 3. Plot the two trajectories on one graph depicting the intercept by a marker (see figure below for example). Label the graph appropriately with units. Give legend and title to graph. Note: Include sufficient comments in the script file so one can understand what the various statements in the code mean. Program should work when using different input variables, so try other variables Submit the following: This sheet signed and on top of all other printouts. Printout of the MS Word file, script file and output graph. . Printout showing the answers to questions listed above in the command window Email the script file and MS word file as attachments. Email once only since only the first email will be accepted so be careful. P19 Project 2 ero

Answer 1

Expression for the time of flight of the projectile, 1. 2v, sin θ Time taken for P^ to raach at a height h is, Time taken for P3 to reach at a height h is, Assume the both time is same, 0.4 OB 500 450 sin 50 60,--58.33°

Expression for the maximum range of the projectile is 2. 0.4 0.4 R= 500x sin 100 9.8 R = 25.12km Time of flight, 3. 2voa sin 6o4 T= 2x500xsin 50 9.8 T=78.16sec

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