What is the Fireworks problem?
Before begining our quadratics unit at the start of the year we were given this problem without any information on how to solve it and were told to just list our observations. Afterwards we began to look at the skills that would be necessary to solve this problem it took a while but once we finished the unit we revisited the problem. This time the entire problem felt much clearer and everything we were confused about became much clearer at the second look.
The Frieworks problem: The jefferson junior varsity soccer team has just won the championship. To celebrate this triumph the school will be putting on a fireworks display. The fireworks will be launched from the top of a school tower. The director isn't concerned about cost, but he wants your help with the timing mechanism that detonates the fireworks, and he's also worried about the saftey of spectators.
What your'e trying to find: You're trying to find when the fireworks will reach their peaks and where the fire works will land/the distance.
What your'e trying to find: You're trying to find when the fireworks will reach their peaks and where the fire works will land/the distance.
H(t)= 160+92t-16t^2 D(t)= 92t/tan 65
Height(time) Distance(time)
Height(time) Distance(time)
First attempt
My group and I's first attempt was unsuccessful. Kinda. At first look we decided it would be a good idea to to plug in number for T starting from 0 to find a pattern or something. After sworking on this for a while I took a closser look at the problem to gain more understanding, we found out we are actually just looking for the x intercepts and the vertex, so that made it a lot easier.
Figuring out the problem
Before we began figuring out the problem we drew a diagram that includes all the information we already knew to kind of help us visualize what was going on.
The first thing me and my group did to start solving the fireworks problem was we found the x intercepts, which are (-1.4,0) and (7.15,0) First of all, we re-wrote the problem in a "way we undertand" Then we found the x intercepts by using the "Bad Boy" method we learned during our quadratics unit. What you do is you plug in numbers from the problem your trying to solve into the "bad boy" formula ( I promise this will make more sense when you look at the pictures) The X intercepts in this case would be representing the time the fire works would land.
After we found the time we needed to figure out the vertex, or the peak of the fire works. To figure this out I added both x intercepts together then divided the answer by 2. The number we got after that is what we plugged in for t. The number we got was 2.875. We solved the equation and the number we got was 292.26 . The final vertex is (2.875, 292.26)
The final thing we did was solve for the final distance which was honestly fairly simple all we did was plug the time/x intercept for t and press the tan button on the calculator.
Problem evaluation
To be completly honest I really did enjoy this problem. It allowed me to use my skills that I learned during the quadradic unit, but it was also challenging and I struggled with it at points. I think that seeing the problem before and after learning the proper skills to solve it was like very fun and interesting becuase I remember being very confused when first seeing it and I didn't really know how to solve it. After mastering in quadradics and looking at the problem for a second time I felt a lot more comfortable and lost all that confusion which was an amazing feeling.
Self evaluation
I would personally give myself a pretty high grade. I think that I did a good job at always staying on task and was always willing to keep trying. I made sure that I tried to include and help my classmates as much as I could.