Ch0108 - Chapter 8 One-Dimensional Motion: Collision Type...

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Chapter 8 One-Dimensional Motion: Collision Type II 43 8 One-Dimensional Motion: Collision Type II A common mistake one often sees in incorrect solutions to collision type two problems is using a different coordinate system for each of the two objects. It is tempting to use the position of object 1 at time 0 as the origin for the coordinate system for object 1 and the position of object 2 at time 0 as the origin for the coordinate system for object 2. This is a mistake. One should choose a single origin and use it for both particles. (One should also choose a single positive direction.) We define a Collision Type II problem 1 to be one in which two objects are moving along one and the same straight line and the questions are, “When and where are the two objects at one and the same position?” In some problems in this class of problems, the word “collision” can be taken literally, but the objects don’t have to actually crash into each other for the problem to fall into the “Collision Type II” category. Furthermore, the restriction that both objects travel along one and the same line can be relaxed to cover for instance, a case in which two cars are traveling in adjacent lanes of a straight flat highway. The easiest way to make it clear what we mean here is to give you an example of a Collision Type II problem. Example 8-1: A Collision Type II Problem A car traveling along a straight flat highway is moving along at 41 . 0 m/s when it passes a police car standing on the side of the highway. 3 . 00 s after the speeder passes it, the police car begins to accelerate at a steady 5 . 00 m/s 2 . The speeder continues to travel at a steady 41 . 0 m/s. (a) How long does it take for the police car to catch up with the speeder? (b) How far does the police car have to travel to catch up with the speeder? (c) How fast is the police car going when it catches up with the speeder? We are going to use this example to illustrate how, in general, one solves a “Collision Type II Problem.” The first step in any “Collision Type II” problem is to establish one and the same coordinate system for both objects. Since we are talking about one-dimensional motion, the coordinate system is just a single axis, so what we are really saying is that we have to establish a start line (the zero value for the position variable x ) and a positive direction, and we have to use the same start line and positive direction for both objects. A convenient start line in the case at hand is the initial position of the police car. Since both cars go in the same direction, the obvious choice for the positive direction is the direction in which both cars go. 1
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Ch0108 - Chapter 8 One-Dimensional Motion: Collision Type...

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