Consider the trajectory of a particle in the gravitational field in R3 which satisfies the following equations: r"(t) = (0, 0, -1), r"(0) = (v1, V2, V3), r(0) = (0, 0, 0), where v3 > 0. (a) Find r(t). (b) Find the x-range of the particle when it hits the ground z = 0. (c) Assume that the initial speed is one, i.e. v2 + v2 + v, = 1. By varying v1, 12, V3, find the maximum x-range when the particle hit ground