$(7.)[15$ points$]$ Home plate of a baseball diamond is located at the origin of an $xyz-$axis. Assume the positive $x-$axis points east and the positive $y-$axis points north. A baseball is hit $2$ ft above home plate with an initial velocity of $($:$40,20,40$:$)f\frac{t}{s}.$ The spin on the ball produces a horizontal acceleration of the ball of $+4f\frac{t}{s^2}.$ The acceleration due to gravity is $-32f\frac{t}{s^2}.$ Determine $a(t),v(t),$ and $s(t).$