Suppose r(t) = cos(πt)i + sin(πt)j + 5tk represents the position of a particle on a helix, where z is the height of the particle. (a) What is t when the particle has height 20? t = 4 (b) What is the velocity of the particle when its height is 20? v = <0,-4,5> (c) When the particle has height 20, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line. That is, the particle should be at the point on the helix at the same time it is starting its motion along the tangent line [the value of t you gave in part (a)], effectively creating a piece-wise defined function for this motion. L(t) = cos (4pi)i (t - 4)j + 5tk Jote: You can earn partial credit on this problem

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