One end of a string of length \(\ell\) is attached to a small ball, and the other end is tied to a hook in the ceiling. A nail juts out from the wall, a distance \(d(d<\ell)\) below the hook. With the string straight and horizontal, the ball is released. When the string becomes vertical it meets the nail, and then the ball swings upward until it is directly above the nail.

(a) What speed does the ball have when it reaches this highest point?

(b) Find the minimum value of \(\ell\) such that the ball can reach this point at all.