Seite - 12 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Band Second Edition

12 1 TheFirstFewSteps Whataboutunits? The observant reader has noticed that the handling of quantities inball.py didnot includeunits, even thoughvelocity (v0), acceleration(g) and time(t) of course do have the units of ms−1, ms−2, and s, respectively. Even though therearetoolsa inPythontoincludeunits, it isusuallyconsideredoutofscope inabeginner’sbookonprogramming.Soalso in thisbook. a See, e.g., https://github.com/juhasch/PhysicalQuantities, https://github.com/hgrecco/pint and https://github.com/hplgit/parampool ifyou are curious. 1.3 APythonProgramwithaLibraryFunction Imagine you stand on a distance, say 10.0m away, watching someone throwing a ball upwards. A straight line from you to the ball will then make an angle with the horizontalthat increasesanddecreasesastheballgoesupanddown.Letusconsider the ball at a particular moment in time, at which it has a height of 10.0m. What is theangleof the line then? Well,wedoknow(with,orwithout,acalculator)thattheansweris45◦.However, when learning to code, it is generally a good idea to deal with simple problems withknownanswers.Simplicityensures that theproblemiswell understoodbefore writing any code. Also, knowing the answer allows an easy check on what your codinghasproducedwhen theprogramis run. Before thinking of writing a program, one should always formulate the algo- rithm, i.e., the recipe for what kind of calculations that must be performed. Here, if the ball isx m away andy m up in the air, it makes an angle θ with the ground, where tanθ=y/x.Theangle is then tan−1(y/x). The Program Let us make a Python program for doing these calculations. We introduce names x and y for the position data x and y, and the descriptive name anglefor theangleθ.Theprogramisstoredinafileball_angle_first_try.py: x = 10.0 # Horizontal position y = 10.0 # Vertical position angle = atan(y/x) print((angle/pi)*180) Before we turn our attention to the running of this program, let us take a look at one new thing in the code. The line angle = atan(y/x), illustrates how the functionatan, corresponding to tan−1 in mathematics, is called with the ratioy/x as argument. The atan function takes one argument, and the computed value is returned from atan. This means that where we see atan(y/x), a computation is performed (tan−1(y/x)) and the result “replaces” the text atan(y/x). This is actually no more magic than if we had written just y/x: then the computation of