enumeration with [(a)]

Question

I am trying to (a), (b), (c) enumeration but when I add [(a)] next to \begin{enumerate} as \begin{enumerate}[(a)], it is not making enumeration.

Could you please help me about solving this problem?

Thank you in advance.

  \begin{enumerate}
    \item Suppose $m$ = 6 kg, $k$ = 3 kg/sec. How high will the projectile go? When will it return to 
        earth, i.e., to $y$ = 0?
        \item Suppose $m$ = 12 kg, $k$ = 3 kg/sec. How high will the projectile go? When will it return to 
        earth?
        \item When $k$ = 0, i.e., there is no air resistance, the equation governing the motion yield $$
        \bar{v} = -gt + v_0, \bar{y} = -\frac{ g t^2 }{ 2 } + v_0 t
        $$
        where the $\bar{v}$ and $\bar{y}$ are the values of the velocity and position when $k$ = 0. 
        Let $v_0$ = 25 m/sec. and $m$ = 6 kg. Now let successively $k$ = 1, 0.1, 0.001, 0.0001 and calculate 
        the return times and compare them with the return time 
        for $k$ = 0. The numerical evidence should suggest that as $k\rightarrow 0$, the return times converge to the value for $k$ = 0. 
\end{enumerate}

Answer 1

To manage listings i suggest you to add \usepackage{enumitem}. At this moment try to use the options:

\begin{enumerate}[label=(\alph*)]
    \item Suppose $m$ = 6 kg, $k$ = 3 kg/sec. How high will the projectile go? When will it return to 
        earth, i.e., to $y$ = 0?
        \item Suppose $m$ = 12 kg, $k$ = 3 kg/sec. How high will the projectile go? When will it return to 
        earth?
        \item When $k$ = 0, i.e., there is no air resistance, the equation governing the motion yield $$
        \bar{v} = -gt + v_0, \bar{y} = -\frac{ g t^2 }{ 2 } + v_0 t
        $$
        where the $\bar{v}$ and $\bar{y}$ are the values of the velocity and position when $k$ = 0. 
        Let $v_0$ = 25 m/sec. and $m$ = 6 kg. Now let successively $k$ = 1, 0.1, 0.001, 0.0001 and calculate 
        the return times and compare them with the return time 
        for $k$ = 0. The numerical evidence should suggest that as $k\rightarrow 0$, the return times converge to the value for $k$ = 0. 
\end{enumerate}

EDIT :

As @Mico suggested, you should surround the numerical values by $ too and switch the $$ into \[...\] or \begin{equation*}...\end{equation*} (see related topic here). I've also added spaces around ; in your motion equations.

\begin{enumerate}[label=(\alph*)]
        \item Suppose $m = 6$\,kg, $k = 3 $\,kg/sec. How high will the projectile go ? When will it return to earth, i.e., to $y = 0$ ?
        \item Suppose $m= 12$\,kg, $k = 3$\,kg/sec. How high will the projectile go ? When will it return to earth ?
        \item When $k = 0$, i.e., there is no air resistance, the equation governing the motion yield 
        \[
            \bar{v} = -gt + v_0\quad ;\quad \bar{y} = -\frac{ g t^2 }{ 2 } + v_0 t
        \]

        where the $\bar{v}$ and $\bar{y}$ are the values of the velocity and position when $k = 0$. 
        Let $v_0 = 25$\,m/sec. and $m = 6$\,kg. Now let successively $k = 1, 0.1, 0.001, 0.0001$ and calculate  the return times and compare them with the return time for $k = 0$. The numerical evidence should suggest that as $k\rightarrow 0$, the return times converge to the value for $k = 0$. 
    \end{enumerate}