Word+Problem+For+Learning+Activity

**Class Handout:**
Mathematicians in Group: Advanced Math and Trigonometry, Lesson 11 Letter Writing: Solving Parabolic Equations **A SpectroMagic Fireworks Blast!** You are Mr. I. C. Light, the engineer coordinating the SpectroMagic Fireworks Show in Philadelphia, PA, which is a July 4th fireworks display at Penn’s Landing by the Delaware River set to music. Your boss, Ms. Ginny I. Sparks, is requesting information from you so that the music planners can properly coordinate the music with the fireworks display. You know that you launch your fireworks from a height of 1.6 meters above the ground. You also know that the initial velocity your fireworks are launched at is 39.2 meters/second. You have derived the following equation to represent the time-height relationship of your fireworks: height = -4.9t2 + 39.2t + 1.6. You are aware that an individual firework explodes at approximately the highest point. Ms. Sparks also expects July 4th to be a windy night (wind is projected to be moving at approx. 15 miles per hour). She needs to make sure the area around the launch site is clear. You know the path of debris from the firework display can be modeled by the function height = -.04x2 + 2x + 8, (where x is the horizontal distance in feet). She needs you to write her a letter including the following: 1) What is more important to the music planners, the height of the firework when it explodes, or the time at which it explodes? Explain. 2) Do the planners need to know the height? Why? 3) How long after a firework is launched will it explode? (in t seconds) 4) What is the height of a firework when it explodes? (in h meters) 5) How far away from the launch site will the debris land? 6) At least how far away must spectators stand? She also requested that you design a safety poster that she can post around Penn’s Landing explaining why barricades were placed in their locations and how many feet away from the launch site people will be allowed to stand to avoid being hit by debris. She wants you to include a pictorial representation (graph) of the projected debris path as well. Good Luck!