September 21, 2010 IOT POLY ENGINEERING I1-14 DRILL : Hamburger U. At a restaurant, the hamburgers are fried on both sides for 60 seconds each. The frying pan can only hold 2 burgers at a time. What is the MINIMUM amount of time needed to cook 3 hamburgers?

IOT POLY ENGINEERING I1-14 DRILL : Hamburger U. - SOLUTION At a restaurant, the hamburgers are fried on both sides for 60 seconds each. The frying pan can only hold 2 burgers at a time. What is the MINIMUM amount of time needed to cook 3 hamburgers? 1. Fry burgers A and B on ONE side for 60 seconds. 2. Put burger A aside and fry burger B on the other side while frying burger C on ONE side for 60 seconds. Burger B is finished. 3. Fry burger C on the other side while frying burger A on its other side for 60 seconds. A B C

IOT POLY ENGINEERING I1-14 HOMEWORK PROBLEM #1 : SPIDER & FLY Given: A spider and a fly are in a room whose dimensions are 25 feet wide by 15 feet deep by 8 feet high. The spider is on the CEILING and the fly is on the FLOOR. If one corner of the room represents the origin (0,0,0) of an x-y-z coordinate system, then the spider is located at (20,8,-11 ) and the fly is located at (5,0,-7 ). See the given diagram. Problem: What is the MINIMUM DISTANCE that the spider must travel to reach the fly on the floor?

The shortest distance between the spider and the fly is a STRAIGHT LINE of about 17.5 feet, but the spider cannot travel that straight line because the spider cannot fly directly toward the fly on the floor. However, the spider can drop straight down to the floor by its spider silk. The distance to the floor is 8 feet. After the spider reaches the floor, its coordinates will be (20,0,-11). IOT POLY ENGINEERING I1-14 HOMEWORK PROBLEM #1 : SPIDER & FLY - SOLUTION The spider is on the CEILING and the fly is on the FLOOR, but the spider is not directly above the fly.

The Pythagorean Theorem can be used to find the distance between the spider and fly. IOT POLY ENGINEERING I1-15 SUMMARY: The spider would need to travel 8 feet DOWN from the ceiling and 15.5 feet ACROSS the floor for a TOTAL distance of 23.5 feet.

IOT POLY ENGINEERING I1-15 HOMEWORK PROBLEM #2 : SPIDER & FLY Given: A spider and a fly are in a room whose dimensions are 25 feet wide by 15 feet deep by 8 feet high. The spider is on the FLOOR and the fly is on the CEILING. If one corner of the room represents the origin (0,0,0) of an x-y-z coordinate system, then the spider is located at (5,0,-7) and the fly is located at (20,8,-11 ). See the given diagram. Problem: What is the MINIMUM DISTANCE that the spider must travel to reach the fly on the ceiling?

IOT POLY ENGINEERING I1-15 HOMEWORK PROBLEM #2 : SPIDER & FLY - SOLUTION The spider is on the FLOOR and the fly is on the CEILING. The shortest distance between the spider and the fly is a STRAIGHT LINE of about 17.5 feet, but the spider cannot travel that straight line because the spider cannot fly directly toward the fly on the ceiling. The spider will have to travel across the floor, go up a wall, and then travel across the ceiling to the fly. 1. What path should the spider travel toward a wall? 2. Which wall should the spider climb? 3. What path should the spider travel up the wall? 4. What path should the spider travel across the ceiling?

IOT POLY ENGINEERING I1-15 HOMEWORK PROBLEM #2 : SPIDER & FLY - SOLUTION 1. What path should the spider travel toward a wall? 2. Which wall should the spider climb? 3. What path should the spider travel up the wall? 4. What path should the spider travel across the ceiling? 1.Traveling straight and perpendicular toward the closest wall seems logical, but it won’t give the shortest total path. 2.The walls are all 8 feet high so it seems that no wall is better than another. Actually, one wall is better than the rest. 3.Traveling straight up the wall seems logical, but it won’t give the shortest total path. 4. Once the spider reaches the ceiling, it should travel directly toward the fly. This seems logical, and is correct.

This problem can be solved by unfolding the room. IOT POLY ENGINEERING I1-15

IOT POLY ENGINEERING I1-15 TAPE At home, use a scissors to cut your paper as follows: Determine the location of the Fly on all 4 ceilings views.

IOT POLY ENGINEERING I1-15 This model will help visualize the problem.

IOT POLY ENGINEERING I1-15 When the room is folded flat, we can see that the strategy of “directly to a wall, up the wall, and across the ceiling” does NOT give the shortest possible path! They aren’t straight.

IOT POLY ENGINEERING I1-15 Drawing straight lines from the spider’s location to the four fly locations gives shorter paths in all 4 cases, and one of these is the shortest possible path!

2.5 inches represents 25 feet. IOT POLY ENGINEERING I1-15

IOT POLY ENGINEERING I1-10 Problem solving process:

IOT POLY ENGINEERING I1-10 Problems covered in class: 1)Chicken, fox, and feed 2)The old man 3)The blocks 4)The coins 5)Bowling Pins 6)The clock 7)The trains 8)The pentagon 9)The numbered blocks 10)The power plant 11)The prime numbers 12)The army ants 13)The rug 14)The plus sign 15)The spider and fly

IOT POLY ENGINEERING I1-10 Solution Techniques 1)Determine the problem 2)Determine constraints and limitations 3)Brainstorm ideas 1)Draw pictures 2)Make simulations 3)Write equations 4)Make flow charts 5)Eliminate wrong answers 4)Choose a strategy and try to solve 5)Check your answer to see if it is reasonable

IOT POLY ENGINEERING I1-16 METROLOGY is the science of measurement, based on the Greek word ‘metron’. METROLOGY should not be confused with meteorology. With a partner, discuss and make a list of the following: 1.Why do we measure? 2.What do we measure? 3.How do we measure? 4.When do we measure? 5.Where do we measure? 6.Who measures?

IOT POLY ENGINEERING I1-10 Classwork/Homework Name three different types of instruments that are used to make measurements. For each type of instrument determine what they are measuring and how does it work. Example: A ruler measures lengths of an object by having markings that correspond to known length. Example: A thermometer measures temperature of an object by having markings that correspond to the volume of mercury.