Problem Statement
A school wants to have a firework display in order to celebrate that their soccer team won the championship. The director doesn't really care about the cost of the show, but he does care about the safety of the spectators. We know that fireworks will be launched from a 65 degree angle, the initial velocity is 92 ft./sec., and the height of the towers is 160 ft. We have fo find the vertex and the distance that the fireworks will travel in order to know that they spectators will be safe.
Process & Solution
When the class first started this problem I was not around to start it, so I don't have all of the classes intial thoughts and the questions that were asked, I do not have my initial start because when we restarted working on the problem my group memebers already had an idea of what they wanted to do so I didn't really have an "Initial Attempt" on the problem.
Here is a picture of the diagram I drew out with all of the given information.
Finding where the fireworks will land |
to find where the fireworks would land I looked at the formula which is h(t)= 160+92t-16t^2 , I then rearanged the formula so that it would be easier to use when plugging it into the quadratic formula so it is now h(t)= 16t^2+92t+160.
Here are my attempt on solving the equation with the quadratic formula.
by plugging in the quadratic formula I got x= (-1.39,0) and (7.14,0), so that means the fireworks will land after 7.14 seconds but if you round you'll get 7.15 as the landing time.
Now to find where to put the spectators, to find a safe distance to place them to be able to watch the fireworks I plugged in the X intercept of 7.15 in for t in the formula d(t)=92 over tan65.
I then got d(t)=306.73ft, so now you know that the spectators will be able to watch the fireworks safely anywhere over 306.73ft away from the landing area.
I then got d(t)=306.73ft, so now you know that the spectators will be able to watch the fireworks safely anywhere over 306.73ft away from the landing area.
above is a picture of my work
|
|
Finding the vertex
To figure out the highest point the fireworks will go I took the two X intercepts and added them together so -1.39+7.14= 5.75 and then you divide it by 2 because it is in the middle of both x intercepts and get 2.88. Now to find Y, you plug in the 2.88 into our original equation which is 160+92t-16t^2 and you plug in the 2.88 as t and get 160+92(2.88)+16(2.88)^2.
To the side I have my attempt, and what I got by doing standard form was 2.88 because it is the middle of the X intercerpts and 292.32 as the Y intercept.
|
Above is my attempt at using the standard formual to find out the vertx
|
Problem Evaluation
I really enjoyed this problem, it was a perfect problem to help us use all of the formulas and subjects we learned throughout the semester. This problem allowed me to push my thinking to it's maximum point because I feel like I had to think and choose from all of the things we learned and use the ones that would be most helpful and make the problem easier to solve. What I think I got most out of this problem was getting to over all of the things we learned with one huge problem, I feel like it was a great review of the semester.
Self Evaluation
I would give myself a B+ and not an A+ because I feel like if I would've been able to solve this problem on my own I would feel much much more confident about the work I did, but since I didn't I would definetly not like to take credit for all of this hard work, so therefore I am giving myself a B+.
Edits
None