Marianne and Rick’s airplane is being chased by a bad guy in a helicopter. Suppose their trajectories are given by the parametric equations:
rp(t) = (h^7t − 10, t^2 , t + 2i) and rH = (ht^2 , 5t − 6, t^2i) for 0 ≤ t ≤ 5.
Let CP and CH denote the corresponding space curves.
(a) Graph Cp and Ch. Do Ch and Cp intersect?
(b) Do the helicopter and airplane collide? Justify your answer.
(c) If they do collide, what is the angle between their tangent lines at the point of collision?
(d) Describe the velocity and acceleration of each of the vehicles.