Which functions do I have to use to solve this waterfall problem written below?

Which functions do I have to use to solve the problem written below?

Write a script called freefall.m examining the effects of air resistance on a distance travelled by a free-falling object. The object is initially at rest, position y = 0 (y is in the direction of gravity). Determine the distance, y = L that a free-falling object travels from a state of rest for the following cases:

1. Without air resistance
2. With air resistance proportional to the linear power of velocity
3. With resistance proportional to the second power of velocity

Many thanks for the hep in advance!

Answer 1

[Shubham Khatri]

You can solve the problem with the following script. You need to give input in the form of defining value for c(proportionalty constant) , time and mass of the object.

clear;
clc;

 ar0=0; %Air resistance equal to 0
 ar1=c*v;%Air resistance proportional to power 1 of velocity
 ar2=c*v^2 %Air resistance proportional to power 2 of velocity
 g=9.81 %m/s^2 (acceleration due to gravity)
   
 %Boundary Conditions
 u=0;
 s=L;
 
 %Force on body = mg- air resistance
 %the object falls for time t
 %Case1
 L=0.5*(g-0)*t^2
 
 %case2
 
 L=0.5*((mg-c*v)/m)*t^2
 
 %case3
 
 L=0.5*((mg-c*(v^2))/m)*t^2

You can covert it to a function as well. Please go through the follwoing documentation link

https://www.mathworks.com/help/matlab/ref/functions.html