On the surface of the earth, the gravitational field (with \(z\) as vertical coordinate measured in meters) is \(\mathbf{F}=\langle 0,0,-gangle\).
(a) Find a potential function for \(\mathbf{F}\).
(b) Beginning at rest, a ball of mass \(m=2 \mathrm{~kg}\) moves under the influence of gravity (without friction) along a path from \(P=(3,2,400)\) to \(Q=(-21,40,50)\). Find the ball's velocity when it reaches \(Q\).