Suppose r rightarrow (t) = cos t i rightarrow + sin t j rightarrow + 4t k rightarrow represents the position of a particle on a helix, where Z is the height of the particle above the ground. Is the particle ever moving downward? If the particle is moving downward, when is this? When t is in (Enter none if it is never moving downward; otherwise, enter an interval or comma-separated list of intervals, e.g.. (0,3], [4,5).) When does the particle reach a point 12 units above the ground? When t = What is the velocity of the particle when it is 12 units above the ground? v rightarrow = When it is 12 units above the ground, the particle leaves the helix and moves along the tangent. Find parametric equations for this tangent line (pick t so that it is continuous through the time when the particle leaves the helix). X(t) = , y(t) = , z(t) = Note: You can earn partial credit on this problem.
