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Review of Part A. Constant Velocity Pursuit
In Part A, you solved the problem of constant velocity pursuit for the hare and the tortoise. For reference, here is the graphical solution. The algebraic solution is below.
Given: xoh = 0 m |
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Goal: Find the time and position when and where the hare reaches the tortoise.
Solution:
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Write the dvats. |
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Substitute 0s. |
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Apply the meeting condition and solve for the meeting time. |
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Solve for the meeting position. |
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Subsitute given values. |
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Check the solution. |
Part B: Accelerated Pursuit
The Goal: Now we generalize to the case of accelerated pursuit. The tortoise is given an acceleration so that he has a chance of outrunning the hare. Open this animation now. Read the problem description and run the animation. Try a few values of acceleration. You'll need a method to determine the maximum acceleration that the tortoise can have so that the hare catches him. Once you've determined the value of this acceleration, you'll use it to determine when and where the hare catches the tortoise.
Strategy: While you could use the above animation with trial and error to determine a value of the maximum acceleration, that would only be considered your solution if you programmed the animation yourself. Physically--that is, using physics--you could use an algebraic method of solution similar to the one in which the hare and the tortoise both have constant velocities. However, since the tortoise has a non-zero acceleration in the present problem, you'll have to include that acceleration in your solution. Solving for time won't be quite as simple; you'll need to use the quadratic formula. In the past, students have used other methods of solution. Unlike previous problem assignments, we're giving you some latitude to design and implement your own strategy.
Design: You'll eventually work within a small group to solve the problem. However, first you'll put some thought in what your strategy of solution will be. We call this the Design phase. You're not required to solve the problem completely in this phase. Instead, you'll decide on a strategy that you think will work. This will involve some brainstorming with pencil and paper at hand. Timewise, about half an hour will be sufficient for this, including the presentation described next.
Presenting your design: Once you've decided on a strategy that you think will be fruitful and that you can implement, clearly describe it. You have at your disposal a variety of represenations: sentence/paragraph form, sketches, graphs, equations. Use what you need to express yourself clearly. The teacher will read what you write and use that as a basis for assigning you to a small group.
Present your design in WebAssign P105B by the due time.
More to come...