Suppose \vec{r}(t) = \cos\!\left(\pi t\right)\boldsymbol{i}+\sin\!\left( \pi t\right)\boldsymbol{j}+5t\boldsymbo l{k} 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 ?
B) What is the velocity of the particle when its height is 20 ?
C) When the particle has height 20 , it leaves the helix and moves along the tangent line at the constant velocity. 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.