Someone2841
New member
- Joined
- Sep 7, 2011
- Messages
- 35
Someone asked me about a solution to this problem:
Given the initial position \(\displaystyle (0,0)\) and constant speed \(\displaystyle v_p\) of the police officer and the initial position \(\displaystyle (x_0, y_0)\) and constant velocity \(\displaystyle v_c\) parallel the x-axis of the criminal, let \(\displaystyle (x_p(t), y_p(t))\) represent the position of the police officer and \(\displaystyle (x_c(t), y_c(t))\) represent the position of the criminal at time \(\displaystyle t\). Is there an angle \(\displaystyle \theta\) and time \(\displaystyle t_1\) such that \(\displaystyle (x_p(t_1), y_p(t_1)) = (x_c(t_1), y_c(t_1))\)?
Does the document linked to below outline the solution to the stated problem? (Note: It only finds \(\displaystyle t_1\). Also, I wouldn't exactly call it "rigorous," but feel free to point out any bad assumptions I may have made, whether or not they affect the solution.)
https://docs.google.com/document/d/1-GH5ZXMVeGnHM1_QfYTZzfFItAzBf5d7LHUzWEF_HdQ/edit
Given the initial position \(\displaystyle (0,0)\) and constant speed \(\displaystyle v_p\) of the police officer and the initial position \(\displaystyle (x_0, y_0)\) and constant velocity \(\displaystyle v_c\) parallel the x-axis of the criminal, let \(\displaystyle (x_p(t), y_p(t))\) represent the position of the police officer and \(\displaystyle (x_c(t), y_c(t))\) represent the position of the criminal at time \(\displaystyle t\). Is there an angle \(\displaystyle \theta\) and time \(\displaystyle t_1\) such that \(\displaystyle (x_p(t_1), y_p(t_1)) = (x_c(t_1), y_c(t_1))\)?
Does the document linked to below outline the solution to the stated problem? (Note: It only finds \(\displaystyle t_1\). Also, I wouldn't exactly call it "rigorous," but feel free to point out any bad assumptions I may have made, whether or not they affect the solution.)
https://docs.google.com/document/d/1-GH5ZXMVeGnHM1_QfYTZzfFItAzBf5d7LHUzWEF_HdQ/edit