"If you have ever spent any time in a wilderness area, you have likely wondered..."
This is a focus problem my teacher gave us. I have no idea how to start it and I do not understand it at all.
If you have ever spent any time in a wilderness area, you have likely wondered about the animals there and your safety. Could you stumble upon a bear on a path in the woods? Could you accidentally come between a moose and her calf? What should you do? It's said that you should never run from a bear, for example, but is that always true? What if the bear is far enough away from you that you think you can get away before it catches you? How far away would you need to be in order to be safe?
Obviously, any serious consideration or calculation has to be done well before you actually encounter a wild animal and must face this decision. We know the top speed at which many animals can run, and we know how long they are able to maintain that top speed. This information is shown in the table for a few animals.
Let's assume that the average person can run 10 miles per hour (at least for short distances while being chased). Let's also assume that a person and an animal each achieve top speed immediately. Determine how much of a head start you would need in order to escape from each animal listed in the table if it was chasing you at full speed. From which animal would you need the greatest head start? Consider that each animal can maintain its top speed for only a certain distance. You can use that distance to determine how long the animal can run and, therefore, how much time it has to catch you. How far can you run in that time? When you calculate the head start that you would need, you are determining the minimum safe distance to be away from that animal. This is useful information to know before heading into that animal's natural habitat. Choose one of the animals listed in the table and write an equation to model its distance run vs. time. Write a separate equation to model your distance from the animal vs. time. Graph both of these equations on the same coordinate grid. Explain how the graphs illuminate the situation. What does the slope represent Where do the graphs intersect, and how do you interpret that point? What do they-intercepts represent? Finally, choose another animal that you are interested in and find the minimum safe distance from it. When we're considering running from a wild animal or head*ing into its natural habitat, we have to consider ...
This focus problem can be solved in many different but related ways. You might begin by trying to understand the issues numerically by "running the numbers." At some point, though, you might discover that representing the information in equations might be more efficient. And, if you're trying to explain what you've discovered about the issues to someone else, a graph might be the most useful way to do it. It's important that you can use multiple representations not only to solve a problem but also to explain your solution to an audience. This is true for the focus problem as well as for many other problems that you'll solve during this cycle. The question "When is it worth it?" will be the focus of the third cycle of the book. Sometimes the focus will be on determining when it is worth it to use algebraic methods.
1.) If the..(pick an animal from the table) can run at...(state top speed and distance), then it can maintain its top speed for...(state time) as shown in the following calculation:
2.) In this time, a person running at 10mph could run... (state time), as shown by the following calculation:
3.) If the animal can run..(state distance) and the person can run...(state distance) in this time, then the person needs to be atleast (calculation safe distance) from the animal to be safe.
4.) *table*
5.) From the table, we can see that you would need the greatest head start if you were running from...(state animal)
6.) The distance run by..(state chosen animal from the table) can be modeled by the equation...(state equation and define variables)
7.) The person's distance run can be modeled by the equation... (state equation and define variables)
8.) The slopes of the lines represent.. (explain slopes). The y-interecepts... (explain y-intercepts). From the grph of these two functions shown below, we can see that the lines intersect at...(state intersection and explain its significance).
9.) graph
10.) A...(choose another animal not given in the table) can run at a top speed of...(state top speed and distance). Thus you would need a head start if... (calculate and state the head start)
This is a focus problem my teacher gave us. I have no idea how to start it and I do not understand it at all.
If you have ever spent any time in a wilderness area, you have likely wondered about the animals there and your safety. Could you stumble upon a bear on a path in the woods? Could you accidentally come between a moose and her calf? What should you do? It's said that you should never run from a bear, for example, but is that always true? What if the bear is far enough away from you that you think you can get away before it catches you? How far away would you need to be in order to be safe?
Obviously, any serious consideration or calculation has to be done well before you actually encounter a wild animal and must face this decision. We know the top speed at which many animals can run, and we know how long they are able to maintain that top speed. This information is shown in the table for a few animals.
Let's assume that the average person can run 10 miles per hour (at least for short distances while being chased). Let's also assume that a person and an animal each achieve top speed immediately. Determine how much of a head start you would need in order to escape from each animal listed in the table if it was chasing you at full speed. From which animal would you need the greatest head start? Consider that each animal can maintain its top speed for only a certain distance. You can use that distance to determine how long the animal can run and, therefore, how much time it has to catch you. How far can you run in that time? When you calculate the head start that you would need, you are determining the minimum safe distance to be away from that animal. This is useful information to know before heading into that animal's natural habitat. Choose one of the animals listed in the table and write an equation to model its distance run vs. time. Write a separate equation to model your distance from the animal vs. time. Graph both of these equations on the same coordinate grid. Explain how the graphs illuminate the situation. What does the slope represent Where do the graphs intersect, and how do you interpret that point? What do they-intercepts represent? Finally, choose another animal that you are interested in and find the minimum safe distance from it. When we're considering running from a wild animal or head*ing into its natural habitat, we have to consider ...
This focus problem can be solved in many different but related ways. You might begin by trying to understand the issues numerically by "running the numbers." At some point, though, you might discover that representing the information in equations might be more efficient. And, if you're trying to explain what you've discovered about the issues to someone else, a graph might be the most useful way to do it. It's important that you can use multiple representations not only to solve a problem but also to explain your solution to an audience. This is true for the focus problem as well as for many other problems that you'll solve during this cycle. The question "When is it worth it?" will be the focus of the third cycle of the book. Sometimes the focus will be on determining when it is worth it to use algebraic methods.
1.) If the..(pick an animal from the table) can run at...(state top speed and distance), then it can maintain its top speed for...(state time) as shown in the following calculation:
2.) In this time, a person running at 10mph could run... (state time), as shown by the following calculation:
3.) If the animal can run..(state distance) and the person can run...(state distance) in this time, then the person needs to be atleast (calculation safe distance) from the animal to be safe.
4.) *table*
5.) From the table, we can see that you would need the greatest head start if you were running from...(state animal)
6.) The distance run by..(state chosen animal from the table) can be modeled by the equation...(state equation and define variables)
7.) The person's distance run can be modeled by the equation... (state equation and define variables)
8.) The slopes of the lines represent.. (explain slopes). The y-interecepts... (explain y-intercepts). From the grph of these two functions shown below, we can see that the lines intersect at...(state intersection and explain its significance).
9.) graph
10.) A...(choose another animal not given in the table) can run at a top speed of...(state top speed and distance). Thus you would need a head start if... (calculate and state the head start)
