P105A. Pursuit Problems

P105A. Pursuit Problems Part B:The Hare and the Tortoise

You'll solve a problem individually tutorial style on WebAssign. Then you'll solve a more challenging problem in a small group.

Part A. Constant Velocity Pursuit

You've had practice now in using graphs of motion as well as in using dvat formulas to solve problems. We combine the two approaches in a category of problems called pursuit problems. The basic idea is that something tries to catch something else. Example 2-9 in your text is a pursuit problem about catching a speeder.

In Part A of P105, you'll be led through the solution of a problem that you may have seen before. Here's the problem:

The tortoise and the hare are having a race. The hare runs at 10 m/s and the tortoise at 1 m/s. The tortoise is given a head start of 100 m. Both start racing at the same time. When and where does the hare catch up to the tortoise?

A bit of history and math... A variation of this problem was posed around 450 BC by Zeno of Athens. He posed it as a paradox: When the hare has run the 100 m, the tortoise has run 10 m. When the hare has run that 10 m, the tortoise has run another 1 m, and so on. How can the hare ever catch the tortoise? The resolution of the paradox is that an infinite series of steps can have a finite sum. In this case, 100 + 10 + 1 + 0.1 + ... = 111.111, repeating (or 1000/9). You may have already studied such series in a math class.

You'll do the problem in tutorial style on WebAssign. This is a type of problem you haven't had before, so we'll describe how it works. The steps of the problem will be presented to you one at a time in the WebAssign interface. Keep the following in mind as you work.While you're given the option to skip a step, don't do so, because you can't back up and you'll lose credit for that step. Always submit your answers. You have two tries for each blank within a step. Once you've submitted all the responses for a step, scroll down to page to see if you were correct. Whether or not you were correct, you'll know the correct answers as a foundation for the steps to follow. That keeps any mistakes from building on each other. It's similar to a teacher standing at the board and leading you through the solution of an example problem step-by-step. While the steps are intended to be simple, you may occasionally come across one that seems difficult to you. In such a case, don't dwell on it and waste time. Enter something and submit. If you get the answer wrong, at least you'll know the right answer immediately and you can continue progress. Don't worry about losing the minor amount of credit that each part is worth, with this exception: Free response items typically count more than objective response. Always take time to express your thoughts clearly and completely in a free-response item.

Here's something to realize about the way language is used in physics and math. Frequently throughout this course, you'll see a statement like, "Express your equation in terms of these symbols only: " This statement will be followed by a list of algebraic symbols. In such cases, your expression may contain no algebraic letter symbols other than those listed. Your expression won't necessarily include all the listed symbols, but it can include no others. It is possible that the expression will include a constant number and, of course, there will be standard operator symbols. Here's an example:

Problem: Express the volume, V, of a cylinder in terms of these symbols only: height, H, and diameter, D, of the cylinder.

Answer: V = (π/4)D²H

In the above, the only algebraic letter symbols used are the allowed ones, D and H. A constant, π/4, is used.

You'll go to WebAssign next to do P105A. Note that this is a prerequisite assignment to P105B. For the latter, we'll present a bit more difficult problem that you'll solve in small groups. We require that you complete P105A first so that you'll be prepared to contribute productively to your group solution.

The Part B problem will be made available after Part A comes due.You'll be assigned a group to work with to devise a strategy for solving the problem.