A rocket is launched vertically. At time $t=0,$ the rocket's engine shuts down. At that time, the rocket has reached an altitude of $450m$ and is rising at a velocity of $130\frac{m}{s}.$ Gravity then takes over. The height of the rocket as a function of time is

$h(t)=(-\frac{5\mathrm{.}4}{2})t^{{?}^{{?}^{?}}}2+130t+450$ for $t>0$

$($a$)$ Create a function called height that accepts time as an input and returns the height of the rocket. Use your function in your solutions to parts $b$ and $c.$

$($b$)$ Plot height versus time for times from $0$ to $30$ seconds. Use an increment of $0\mathrm{.}5$ second in your time vector.

$($c$)$ Find the time when the rocket starts to fall back to the ground. $($The max function will be helpful in this exercise.$)$