A student club is designing a trebuchet for launching a pumpkin into projectile motion. Based on an analysis of their design, they predict that the trajectory of the launched pumpkin will be parabolic and described by the equation y$($x$)=$ax$^2+$bx

where a$=8\mathrm{.}0$times $10^(-3)$ m$^(-1)$

$,$ b$=1\mathrm{.}0($unitless$)$

$,$ x is the horizontal position along the pumpkin trajectory and y

is the vertical position along the trajectory. The students decide to continue their analysis to predict at what position the pumpkin will reach its maximum height and the value of the maximum height.

Determine the times at which v$($t$)$ has a local minimum and maximum.

What are the corresponding minimum and maximum velocities that the rocket experiences?