Problem Two

Simple Function: Write a MATLAB function that contains the following items. Remember to apply function concepts that we discussed in class. This function will determine the terminal velocity of a cloud droplet based on Stokes' law. According to this law, a droplet reaches its terminal velocity when gravitational $(F_G)$ and drag $(F_D)$ forces are opposite and equal to each other in magnitude.

Use droplet$\_$velocity as your function name. Your function definition line is your first line of code. There should be no code, including comments, above this.

The function has one input: $r,$ which is radius of the droplet$($s$)$ that you will be calculating the terminal velocity for.

The function will have two output values: $v,$ the terminal velocity of the droplet$(s)$ and $t,$ the time that the droplet$($s$)$ to fall

Your function will have a help block that describes the details of the function. This includes what the function does and a description of the input and outputs. Student header information should also be found here.

Your function will calculate the terminal velocity for the droplet$($s$).$ Keep in mind that $F_G$ and $F_D$ are equal and opposite, so setting these two quantities equal to one another is the first step towards calculating $v.$

Using the velocities calculated and ignoring the droplet growth, your function will then estimate the time required for each droplet to fall in a cloudy air with a height of $1454$ ft $.$ This is the height of the Empire State Building, including its spire and antenna.

Your function should work for scalar, vector and $2$D array input. To determine, carefully consider if$/$when the dot operator may be needed. Try it on inputs that are vectors. i$.$e$.$ Have it calculate for several droplet radius values at once.

At the command window, you will test your function with $r=[2,15,30]m$ in radius.

Include, as comments at the end of your file:

Your function call $($What did you type in the command window to run this function?$)$

The results from when $r=[2,15,30]m$