The fighter plane of Exercise 59 travels along the path r(t) = (t − t³, 12 − t², 3 − t). Show that the pilot cannot hit any target on the x-axis.

Data From Exercise 59

A fighter plane, which can shoot a laser beam straight ahead, travels along the path r(t) = (5 − t, 21 − t², 3 − t³/27). Show that there is precisely one time t at which the pilot can hit a target located at the origin.