Instructions:

In addition to this document, you will also need the two excel files ProjectileData.xlsx and

HydrogenPeroxide.xlsx$.$ The files are on Moodle in the Curve Fitting and Interpolation topic area

$($same general location where you found this file.$)$ Put both of this files in your current MATLAB

directory.

Problem $1$: Curve Fitting $$ Trajectory of Projectile

The excel file, ProjectileData, has three columns of data: time, distance, and height. Import

ProjectileData.xlsx into MATLAB. The distance variable represents measurements of the x

position $($horizontal position$)$ of the projectile over time and the height variable represents

measurements of the y$-$position $($vertical position$)$ of the projectile over time.

The equations for the x and y positions of a projectile launched at an angle of $\backslash$theta $($degrees$)$ with an

initial velocity of V$0($m$/$s$)$ are:

a$)$ Plot time on the x$-$axis and distance on the y$-$axis. Add axis labels $($with units$)$ and a

title to your plot. We know that the x$-$position of the projectile increases linearly with

time. So$,$ use the curve fitting tool to fit a $1$st order polynomial $($line$)$ to the distance

data. Display the equation for the fitted polynomial on your graph with $5$ significant

digits. Submit through Moodle your $.$fig file as well as your script $(.$m or $.$mlx$)$ for

automating the generation of the plot.

b$)$ Plot time on the x$-$axis and height on the y$-$axis. Add axis labels $($with units$)$ and a title

to your plot. We know the height of the projectile follows a parabolic $(2$nd order$)$ curve.

So use the curve fitting tool to fit a $2$nd order polynomial $($quadratic$)$ to the height data.

Display the equation for the fitted polynomial on your graph with $5$ significant digits.

Submit through Moodle your $.$fig file as well as your script $(.$m or $.$mlx$)$ for automating the

generation of the plot.

c$)$ Look at the numerical coefficient for the squared term in the fitted polynomial for the

height data. Theoretically, this coefficient should be equal to $-1/2*$g$.$ How close is it$?$

Calculate the percent error using the following formula with $-1/2*$g as actual value:

Using good programming practices, create a script that allows for the inputting of the

estimated value $($numerical coefficient for the squared term$)$ then calculates and displays

the $\%$error. Submit your solution using the Moodle Curve Fitting Homework submittal

link.

$1$

$2$

d$)$ The numerical coefficient for the linear term in the fitted polynomial for height should

be approximately V$0$ sin$(\backslash$theta $)$ and the numerical coefficient for the linear term in the fitted

polynomial for distance should be approximately V$0$ cos$(\backslash$theta $).$

V$0$ sin$(\backslash$theta $)=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

V$0$ cos$(\backslash$theta $)=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$\backslash$theta $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($include units$)$

V$0=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($include units$)$

Using good programming practices, create a script that allows for the inputting of the V$0$

sin$(\backslash$theta $)$ and V$0$ cos$(\backslash$theta $)$ values, and then calculates and displays the launch angle, $\backslash$theta $,$ and

initial velocity, V$0.$ Submit your solution using the Moodle Curve Fitting Homework

submittal link.

Hint: Solve for launch angle by dividing $($V$0$ sin$(\backslash$theta $)/$ V$0$ cos$(\backslash$theta $)).$ This value is equal to

the tan$(\backslash$theta $).$ Thus taking the arctan or tan$-1$ of the value will result launch angle. Using

the angle and value for V$0$ sin$(\backslash$theta $)$ or V$0$ cos$(\backslash$theta $),$ you can then calculate the initial velocity,

V$0.$