# A free fall motion of an object

Developing a Scilab Code to: Solution to a free fall motion of an object
Consider an object in a free fall vertical motion. The motion is analysed in three conditions;

The object motion is analysed without friction (air resistance).

Equations of motion:

ya=1/2 gt^2 displacement of the free fall

va=gt velocity of the free fall

aa=g acceleration of the fee fall

The motion is analysed with the effect of air resistance (friction) that is proportional to the linear power of velocity.

Equations of motion:

yb=g/k t-g/k^2 (1-e^(-kt) ) displacement of the free fall

vb=g/k (1-e^(-kt) ) velocity of the free fall

ab=g-kv acceleration of the fee fall

The object is analysed with the effect of friction that is proportional to the second power of velocity.

Equations of motion:

yc=1/k log[cosh⁡(gkt/2)] displacement of the free fall

vc=1/2 g/k tanh(gk/2 t) velocity of the free fall

ac=g-kv^2 acceleration of the fee fall

The Scilab programme should calculate the object displacement (distance travelled from the origin y=0), velocity and acceleration in free fall motion. The calculations should be conducted for all three configurations a, b, and c, (in one single code). The calculated quantities (y, v, and a) should be plotted against time array; t= 0 – x
where;
x = last digit of your student ID – Note: if the last digit=0, then take the second to last digit, and if the second to last = 0, take the third to last digit.
Also, if 1 x  4 then the time array should be taken as; t = 0 – (x+1)2
K – is the air friction coefficient = 0.x (x = last digit of your student ID – Note: if the last digit=0, then take the second to last digit, and if the second to last = 0, take the third to last digit.

Procedure of developing the Scilab programme:
The initial conditions for all three cases are; y=0, t=0, v=0
All three cases should be built in one single code (you may break the code into three sections; a, b, c)
For each case the motion parameters (y, v, a) should be assigned to different letters – e.g. for case ‘a’ (analysis without friction) the displacement is ‘ya’ and for case ‘b’ (analysis with friction proportional to the linear power of velocity) it is assigned as ‘yb’ and so on.
Type the name of the code at the very first line (don’t forget to use the // (the comment function)
Make the input for the time array; t= 0 – x (where x is the last digit/second to last/third to last digit of your student ID (see note above)). And choose an appropriate time step size t (intervals).
Assign the friction coefficient; k = 0.x (where x is the last digit/second to last/third to last digit of your student ID (see note above))
Assign g=9.81
Starting from case a, make the input for the equations of motion in a correct order (precedence)
Plot the data/graphs in bundles; all displacements from all cases plotted together (ya,yb,yc) vs t; all velocities (va, vb, vc) vs t; all accelerations (aa, ab, ac) vs t. Make good use of the plot commands available in Scilab
Create titles, labels and legends for the graphs.

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