Simple free fall problem
H.Tahsiri
The following is a simple sample problem that shows
the interaction between instructor,student and the
the computer.
1) Instructor role: The instructor lectures on a free
falling object and derives the equations of motion.
He then assigns the following homework problem to
be done by the student.
2) Student's role: The student sit by the computer
and run Mathematica. He then enters the equations of
motion into Mathematica's notebook as shown.
3) Computer's role: Equations of motion are imputed
and can be used for any general free falling problems
in the text.
freefalleqs={eq1=v==v0-g*t,eq2=y==y0+v0*t-1/2g*t^2,
eq3=y==y0+(v+v0)*t/2,eq4=v^2==v0^2-2g*(y-y0)};
Problem: A marble is accidently dropped from the top
of the Sears Tower in Chicago. Cosidering that the height
of the building is 1400 ft and ignoring air resistance, find
the impact speed of the marble with the ground.
given={v0->0,g->32,y0->1400,y->0};
impactspeed=Solve[eq4,v]/.given//N
{{v -> 299.333}, {v -> -299.333}}
accept=Take[impactspeed,{2}]
{{v -> -299.333}}
Student reports the impact speed of 299.333 ft/s downward and he is done.
Instructor role: By adding many possible variations
to the problems,for example adding the air friction,
will lead the students to do a more realistic physical
problem.
Mathemathica commands and their meanings used in this problem
are provided to the students by the instructor.