# Homework Help: Parabola word problem

1. Jul 6, 2011

### NurseLaurie

Hi all. I'm a nurse in the middle of a nightmare math class. It is second half of college algebra but it may as well be Greek. The professor is a PhD in engineering and is teaching way over my head- and others from what I hear. I have never failed a class in my life but this may be a first. We have the following word problem.
I semi understand that if I plot the three points related to the altitude and kilometer. But I don't know how to get to the point where how off shore they are. Are they hitting, are they missing!! It is truly the first time in any class I am lost. This is an online course so hard to get help, plus he tells us not to ask questions he has already answered. Can anyone start me on a path. I have looked at his for 3 hours. Not very productive.

*

The surface of planet Xyz, in a galaxy far away is mostly an ocean of Nitric Acid.* The planet is inhabited by two tribes of human-like creatures, the Blue People and the Green people, who live in separate islands.* They know of each other’s existence because they had a common origin, but because of the corrosive nature of the ocean, they have not made actual contact with each other since the ocean turned acid 10 million years ago.* One hundred years ago, word got out somehow, that these two peoples professed significantly different religious beliefs.* The Blue people’s holy book stated that “thou shall never show your feet” (or something to that effect) and they wore concrete shoes to make sure their feet were never exposed.* The green’s people Holy Scripture stated that sitting down was a mortal sin and disrespectful of God. Well, the scandal that the news ensued was of biblical proportions, as the Green people imagined all those Blue folks sitting down and offending God, while the Blue people were disgusted beyond constraint, thinking of those green and insultingly exposed toes.* Both Islands managed to declare war on the other, not even knowing where the other island actually was. Pacifists from both islands were labeled ungodly and unpatriotic by political leaders and angry radio-show-hosts, and despite their best effort could not stop the nonsense.

Armed with large catapults, they began throwing large rocks decorated with insults, towards the horizon and in all directions, in hopes of destroying the infidels. Their military developed larger and larger catapults, until finally, lookouts in each island began to see the incoming boulders splashing into the ocean.* Now they both knew in what direction to shoot. Realizing their dilemma shots became less frequent. Scouts from both islands were sent out in boats to more precisely determine the path of incoming boulders.* The scouts knew how far they were from their own shore, and they could determine and record the exact altitude of the boulders that passed over their heads.* They reported the following set of data:

At 20 kilometers from shore the incoming boulders were located at 2800 meters of altitude.* At 40 kilometers from shore, they were spotted at 4200 meters of altitude.* And at 70 kilometers out, the boulders were passing at 5550 meters of altitude.

Despite their obvious limitations, Blue and Green scientists had figured out that the trajectories of boulders release by catapults were perfect parabolas.

You are a prisoner of these mad people and to save your own skin, you are required to use the information gathered by the scouts and answer the following questions (in a way that it is clear to them):

1.**** How far from their shore is their enemies catapult?
2.**** Are their shots too short or too long to hit us and by how Much?

Seriously, I have hired a tutor to help me with the calculating of equations and learning formulas, but I don't even know where to start with this.

Thanks for anything you can offer..

Laurie
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 6, 2011

### ehild

Do you know the equation of a parabola?

ehild

3. Jul 6, 2011

### Staff: Mentor

Also draw a diagram where you can mark on all the information you are given: heights, distances, etc. Picture yourself as standing a way off to the side, watching the projectiles as they rise from some distant canon, soar high into the air, then descend towards the enemy.

4. Jul 6, 2011

### HallsofIvy

$y= ax^2+ bx+ c$ where x is a horizontal distance and y is vertical. If you are given three points, put the coordinates of those in for x and y to get three equations to solve for a, b, and c.