Question: If a particle moving along a curved track (like a roller coaster) flies off the track, it continues in the direction of the tangent vector at the point where it left the track, at least if there are no external forces such as gravity or friction acting on it. Suppose a particle rolling down (towards the xy-plane) the helix shaped track given by r(t)=(2 cos t, 2 sin t, t) flies off the track when t = pi/4. Determine the point where the particle will hit the xy-plane.