disc1_solns - Physics 211 Week 1 One-Dimensional Kinematics...

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Physics 211 Week 1 One-Dimensional Kinematics: Bonnie and Clyde (Solutions) In your new job, you are the technical advisor for the writers of a gangster movie about Bonnie and Clyde. In one scene Bonnie and Clyde try to flee from one state to another. If they get across the state line, they could evade capture, at least for a while until they become Federal fugitives. In the script, Bonnie is driving down the highway at 108 km/hr and passes a concealed police car that is 1 km from the state line. The instant Bonnie and Clyde pass the patrol car, the cop pulls onto the highway and accelerates at a constant rate of 2 m/s 2 . The writers want to know if they make it across the state line before the pursuing cop catches up with them. ______________________________________________________________________ Conceptual Analysis: - Since Bonnie and Clyde are traveling at a constant velocity and the cop is accelerating, at a certain place and time, the cop will overtake Bonnie and Clyde. Strategic Analysis: - Create two equations- one describing the motion of the accelerating cop and the other describing the motion of the constant velocity of Bonnie and Clyde. - Pick one of two strategies to solve the problem. You can either a) find the place where they meet to see if it is within the state line or after it, or b) find the time it takes for each to reach the state line to see who reaches it first. - Solve the two equations to find the place where the cop overtakes Bonnie and Clyde or who crosses the state line first, depending on which method you choose to use. Quantitative Analysis: Begin by labeling the given values: v BC speed of Bonnie and Clyde d bord distance from cop to border a c acceleration of cop We will be looking for either x BC distance Bonnie and Clyde travel, and x c distance the cop travels, which are equal where the two cars meet or, using the other method, we will find t BC the time it takes Bonnie and Clyde to reach the state line, and t c the time it takes the cop to reach the state line Next we can create equations to describe the motion of Bonnie and Clyde and the cop. If we choose the initial time and position of the cop to be t o = 0 and x o = 0, then we have the position of Bonnie and Clyde and the position of the cop after time t to be BC: x BC = v BC * t Cop: x c = ½* a c * t 2 - Now you can choose between the two methods as you solve the equations. - Let’s start by solving for the place that they meet. When they meet x BC = x c . Knowing this we can solve:
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v BC * t = ½ * a c * t 2 The time that they are in the same place, t same , then, is t same = 2* v BC / a c Now we can find the place where they are at this time by plugging the time back into either of the position equations: x c = x BC =2* v 2 BC / a c - The other method is to find the time it takes each party to reach the state line. BC:
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disc1_solns - Physics 211 Week 1 One-Dimensional Kinematics...

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