Exercise $1$: You$$re conducting a projectile motion experiment to see if you can predict where

an object will land given an initial height, a final height of $0$ m$,$ an initial y$-$velocity component of

$0$ m$/$s$,$ an acceleration due to gravity of $-9\mathrm{.}81$ m$/$s

$2$

in the y$-$direction, an initial x$-$position of $0$ m$,$

and an initial x$-$component velocity $($in m$/$s$)$ that you$$ve measured with photogates over multiple

trials: $(1\mathrm{.}23,1\mathrm{.}19,1\mathrm{.}25,1\mathrm{.}27,1\mathrm{.}20,1\mathrm{.}22).$

To figure out a range of where the object might land, you need to calculate the standard de$-$

viation for your x$-$component velocity data. Since you will often have to calculate the standard

deviation of multiple trials when conducting experiments, define a standard deviation function

that has an optional, keyword input parameter for whether your function calculates the popu$-$

lation standard deviation, $\backslash$sigma $=$

q$\backslash$Sigma $($v$$vavg$)$

$2$

n

or the sample standard deviation, $\backslash$sigma $=$

q$\backslash$Sigma $($v$$vavg$)$

$2$

n$1$

$,$

and default the value to $1$ for a sample standard deviation so that you can have n $1$ in the de$-$

nominator $($the value will be $0$ for a population standard deviation in order to have only n in

the denominator$).$ Using array syntax, define the function in the first cell, and in the second cell

create an array of the x$-$component velocity values and use the function to calculate the standard

deviation.