Harry Potter is caught in a fierce duel between him and his rival Draco Malfoy. Draco just missed Harry with the Expelliarmus spell and Harry fires back with a Flipendus jinx, attempting to send Draco flying. Harry is standind 12 feet from Draco and shot the spell at an angle of 38 degrees from his wand, which is 4 feet above the ground. The Flipendo jinx travels at a rate of 22 ft/sec. Disarmed, as soon as Harry unleashes the spell, Draco starts to run in the opposite direction at a rate of 6 ft/sec. Will the spell die out before it hits Draco? If not at what value of x will the spell hit Draco? Create 2 sets of parametric equations to model both the spell and Draco running.

Question

Harry Potter is caught in a fierce duel between him and his rival Draco Malfoy.  Draco just missed Harry with the Expelliarmus spell and Harry fires back with a Flipendus jinx, attempting to send Draco flying.  Harry is standind 12 feet from Draco and shot the spell at an angle of 38 degrees from his wand, which is 4 feet above the ground.  The Flipendo jinx travels at a rate of 22 ft/sec.  Disarmed, as soon as Harry unleashes the spell, Draco starts to run in the opposite direction at a rate of 6 ft/sec.  Will the spell die out before it hits Draco?  If not at what value of x will the spell hit Draco?  Create 2 sets of parametric equations to model both the spell and Draco running.