The position of a skier on the mountain as a function of time is given by
$$x(t) = 0.50t^2 + 2.0t$$
$$y(t) = -t^2 + 10\cos(0.50t)+500$$
$$z(t) = 0$$
where the x/y plane is parallel to the surface of the hill with the x-direction pointing across the hill and the y-direction pointing up the hill (with the bottom of the hill being a y-position of zero). The z-direction is normal to the hill.
What is the instantaneous acceleration vector of the skier at a time of $t = 10\space s$?