Consider the trajectory of a particle in the gravitational field in R which satisfies the following...

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Consider the trajectory of a particle in the gravitational field in R which satisfies the following equations: r'" (t) = (0,0, 1), r'(0) = (V1, V2, V3), F'(0) = (0, 0, 0), where v3 > 0. (a) Find F(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. v + v + v/3 find the maximum x-range when the particle hit ground. 1. By varying V1, V2, V3, Consider the trajectory of a particle in the gravitational field in R which satisfies the following equations: r'" (t) = (0,0, 1), r'(0) = (V1, V2, V3), F'(0) = (0, 0, 0), where v3 > 0. (a) Find F(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. v + v + v/3 find the maximum x-range when the particle hit ground. 1. By varying V1, V2, V3,