Suppose the particle of the preceding problem moves instead at constant speed along an isoceles triangular path between the beginning point and the end point, with the high point at height \(z_{1}\) above the ground, at \(x=x_{1} / 2\) and \(t=t_{1} / 2\).

(a) Find the action for this path.

(b) Find the altitude \(z_{1}\) corresponding to the least-action path among this class of constant-speed triangular paths.

(c) Verify that the total action for this path is greater than that of the parabolic path of the preceding problem.