Exercises 4.1 to 4.7:
Feynman Exercises Chapter 04
Computer solution output of Exercise 4.6:
C# source code for the computer solution of Exercise 4.6, sorry about the naming confusion in the file:
Exercise 4.6
Computer solution of Exercise 4.7 using a velocity square drag function (velocity retardation function is the term used in exterior ballistics). I wrote a baseball ballistics program based on my numeric work (Runge-Kutta Fifth Order) and analytic solutions found in the paper:
Click to access 04-LAJPE-782_Chudinov.pdf
The first picture is the main form interface for the program with the parameters initial velocity in meters per second and the initial angle which is in degrees. We use a velocity of 25 meters per second which is approximately 56 miles per hour and the angle is 90 degrees to the horizontal which is throwing the ball straight up into the air.
First we show the classical ballistics without atmospheric drag:
Next we show the invalid (due to a singularity in one of the equations) analytic and numeric solutions:
The analytic solution is not valid for theta0 = 90 degrees. The numeric solution shows a time to apogee of 2.28 seconds and time of flight 4.66 seconds. The difference is 4.66 – 2.28 seconds = 2.38 seconds so the time to return from apogee is greater than the time to reach apogee. The analytic solution becomes valid at 88 degrees of inclination.
Next we move onto an inclination of 15 degrees:
Finally for the maximum distance traveled by the ball classically we select 45 degrees:
We find that with drag the maximum distance traveled (range) is achieved around 43 degrees:
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
View all posts by jamespatewilliamsjr
Numerical Explorations 