**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/sdownward 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.