Parametric Equations (I)
- Tim Brzezinski
Note to instructors: This applet was designed to be seen by students after they've attempted to solve the following problem for a few minutes. (There are various methods of solution to this problem.) Problem: Two ships (Ship A & Ship B) are out at sea. Ship A is currently stationed at (50, 100) and travels in such a way that it moves 3 feet east and 5 feet north every minute. At the same time Ship A is at (50,100), Ship B is at (900,250) and moves 4 feet west and 4 feet north every minute. If both ship captains choose not to alter their courses, will the ships be in danger of crashing in to each other? Show mathematically why or why not. Students: After interacting with the applet below for a few minutes, please answer the questions that follow.
Questions: Let t = the time (in minutes) that pass since the start of this story. So, when t = 0, point A is at (50,100) and point B is at (900, 250). 1) Write a function that gives the x-coordinate of point A as a function of t. 2) Write a function that gives the y-coordinate of point A as a function of t. 3) Write a function that gives the x-coordinate of point B as a function of t. 4) Write a function that gives the y-coordinate of point B as a function of t. 5) Could you have used any one (or more) of these functions you've written for (1) - (4) above to help solve this problem? If so, how? Explain.