problem statement :The Jefferson high school JV 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 on the top of a school tower. The director isn't concerned about the cost, but he wants your help with the timing mechanism that detonates the fireworks, and he's also worried about the safety of spectators.
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Information to solve the problem:
Questions and equations :
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h(t) + 160 + 92t - 16t²
d(t) + 92t/tan65 |
Questions I first had to solve the problem:
How to get the vertex?
How did getting the time helped? |
how can you get to get the x intercepts so we could get the vertex?
Whats aftergetting x intercept ang getting the middle point to get the vertex ( how to solve for it) ? |
My initial attempt :
So my first attempemt was actually good but at the smae time I didnt knew what to do first so I tried to solve for the vertex and the only hint i had it was this equation -> h(t)= 160+92t-16².
First i knew the X intercept were the key to get the vertex but that was my trouble after I asked my teacher and partners. Process for X intercept:For the X intercepts you must do the quadratic formula that we learned a couple weeks before and I am trying to solve for the X intercept because that is gonna help me trying to get the vertex and solving the first question of the problem.
The quadratic formula is an easier way to sole "ax2 +bx+c=0 but sometimes the formula doesnt work when you can factorize it. In this case solving for the cuadratic formula would help us to get the x intercept after you solve the quadtatic formula you probably would get (-1.399,0)(7.149,0). How to solve for the vertexAs we know we are gonna use our X intercepts to get the vertex the middle point of the X intercept its where the X point of the vertex so if our X intercepts are (-1.399,0)(7.149,0) the middle point of them will be 2.875 sec. then you can plug in that 2.875 in the first equation h(t) + 160 + 92t - 16t² you will get 292.95 ft and that wil be your peak ( vertex ) : ( 2.875 sec, 292.25 ft )
How far will the fireworks go:Using the X intercept (7.159, 0) you will need to plug it in in the equation d(t)=92t/tan 65 you will know the distance of how far will the firework will travel you will need to multiply 92 and 7.149 and then divide by tan 65. You will get 306.69 ft and that will be the distance the firework will travel.
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Problem Evaluation
Im gonna say that I did like this problem because it involves most of the things we've been learnign throughout this whole semester but that doesnt mean the problem was easy because I kind of forgot what we learned first and have more knowledge on the recent work so the last part of how to get the vertex even when I think its easier was harder for me at least and I think I learned most out of this part of the problem that makes me remember the thinks we saw first.
Self Evaluation
If I was able to grade myself in this problem I would give me an B or an B+ because I did work hard even when I didn't understood the problem I still asked a lot of questions to the teacher and my partners also the B+ is because a lot of times I used to get distracted but hopefully throughout the time i've been getting more into the class and less distracted because my teacher always reminded me that I should be on task.
What I changed from the feedback I got:
I changed a few pictures because they werent explaining very well what I was talking about and fixed a lot of grammar.