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#excercise_05:chapter2_problem2.9


##@.abstract ######this is programmed to reach a numerical solution to problem2.9 of Nicholas J.Giordano's computational physics。 the eessential points of this problem is:
1.include both air drag and the reduced air density at high altitudes.
2.perform the calculation for different firing angles.
3.determine the value of the angle that gives the maximum range.

##@.background ###1.dynamic equations ###2.drag force and some coefficient ###3.Euler's method ##@.main body:programs and results ######the py_document has been uploaded,click here to check it ###1.the primary part of the program ###2.call the class and the result of it


    this program can print the initial values,landing coordinate and output the cannon trajectory diagram.

###3.perform the calculation for different firing angles.


  there are 88 trajectories which firing angles are 1 degree,2 degrees,......,88degrees.

###4.determine the value of the angle that gives the maximum range.


 this program can print the maximum rang and its firing angle and output a diagram that shows how ranges varies with firing angles 

##@.conclusions #####1.the air resistance have a substantial effect on the trajectory,which is no longer a quadratic curve.
#####2.since there is air resistance,the angle that gives the maximum range is usually less than 45degree.
##@.acknowledgement #####thank to Mr.cai's teaching document