In Figure P$2\mathrm{.}21,$ the plane travels along the vertical parabolic path Y $=0\mathrm{.}4$X$2($note that X and Y are in km$,$ not m$).$ At point A $(5,10)$ km$,$ the plane$$s speed along the path is $280$ m$/$s$,$ and it is decreasing at $1$ m$/$s$2.$

Tasks: At the instant illustrated:

$($a$)$ Determine the velocity and acceleration components in path coordinates.

$($b$)$ Determine the velocity and acceleration components in Cartesian coordinates.

$($c$)$ Determine the velocity and acceleration components in polar coordinates.

$($d$)$ Draw vector diagrams to demonstrate that same velocity and acceleration vectors are obtained for all three$-$coordinate systems. Use figures showing labeled components, unit vectors, and units.FIGURE P$2\mathrm{.}21$