What is the solution to this parabola word problem?

In summary, the speaker is struggling with a difficult college algebra class, specifically a word problem involving plotting points related to altitude and distance. They are lost and have been unable to find help due to the class being online and the professor not allowing repeated questions. The conversation then shifts to a hypothetical scenario involving two tribes on a planet who are at war and attempting to calculate the distance and trajectory of their enemy's catapults using the altitude and distance measurements of passing boulders. The speaker is seeking help and guidance on how to approach the problem.
  • #1
NurseLaurie
1
0
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.




This is due in your Assignment Link by Monday, July 11.* Please, clearly explain your reasoning and your steps.* Please, highlight the numeric answers (just the answers).

*

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

 
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  • #2
Do you know the equation of a parabola?

ehild
 
  • #3
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
[itex]y= ax^2+ bx+ c[/itex] 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.
 

1. What is a parabola word problem?

A parabola word problem is a mathematical problem that involves finding the solution for a scenario that can be represented by a parabola. Parabolas are U-shaped curves that can be described by a quadratic function.

2. How do you solve a parabola word problem?

To solve a parabola word problem, you first need to identify the known values and the unknown value in the problem. Then, you can use the quadratic formula or complete the square method to find the solution. It's important to remember to check your solution to make sure it makes sense in the context of the problem.

3. What are some real-life examples of parabola word problems?

Examples of parabola word problems in real life include calculating the maximum height of a projectile, determining the optimal path for a satellite orbit, and finding the profit-maximizing quantity for a business that follows a quadratic cost function.

4. How do you graph a parabola word problem?

To graph a parabola word problem, you can plot the known points on the coordinate plane and then use the shape of the parabola to estimate the position of the unknown points. You can also use the quadratic formula to find the vertex of the parabola, which can help you accurately graph the curve.

5. What are some strategies for solving difficult parabola word problems?

Some strategies for solving difficult parabola word problems include breaking the problem down into smaller parts, using a graphing calculator to visualize the problem, and trying different problem-solving techniques such as substitution or elimination. It can also be helpful to review similar problems and their solutions to gain a better understanding of the concept.

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