You are here:
- Home
- Teens
- Homework/Study Tips
- Calculus
- Calculus and bugs
Calculus/Calculus and bugs
Advertisement
Question
I can't see how to use calc for the following problem, I can do it with Geometry though, please help.
Consider a room in the shape of a cube, 4 meters on each side. A bug at point P wants to walk to point Q at the opposite corner, Use calculus to determine the shortest path
Consider unfolding the room. The bugs is in the upper corner of one square and where he is walking to is in the lower corner of the adjacent square.
The shortest line is a straight line from one corner to the other.
The length of it would be √(8²+4²) = 4√3.
To do this problem with calculus, consider some point x units from the ground on the corner between them. The total distance travelled would be √[4²+(4-x)²] + √(x²+4²). The function can be reduced to
√[32-8x+x²] + √(x²+16).
To find the minimum, take the derivative and set to 0.
(x-4)/√(32-8x+x²) + x/√(x²+4²) = 0.
As you can see, geometrically, the problem is much easier to find.
Note that the path could be in any of 3 directions. The bug needs to choose one of the adjacent walls or the ceiling. Once this choice has been made, he can walk in any direction to the point halfway along the opposing edge, then walk to the other corner.
--------------------------------------------------------
Just to put in some comedy, note that bugs aren't that bright. They can't even comprehend where they are going and certainly don't care how long it takes to get there. Maybe that makes you smile.
- View Follow-Ups
- Add to this Answer
- Ask a Question
| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |
| Comment | No Comment | ||
Related Articles
- Bank Shots - Score Much More Often On Bank Shots
- Long-line Walking — Teach Your Dog to Go Your Way - Dog Obedience
- Free Quilt Patterns - Oriental Courtyards Quilt Pattern
- Baby Quilt Patterns - Beginner Quilt Patterns - Easy Quilt Patterns
- Free Quilt Block Patterns - Maryland Beauty Quilt Block Pattern
Answers by Expert:
Scotto
Expertise
Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.
Experience
Experience in the area: I have tutored students in all areas of mathematics for over 25 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC.
Well over 2,000 of them have been in calculus.
Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors
I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.
©2012 About.com, a part of The New York Times Company. All rights reserved.