# Parametric Equations (I)

[b][color=#ff0000]Note to instructors: [/color][/b][br][br][color=#000000]This applet was designed to be seen by students [/color][i][color=#ff0000][b]after [/b][/color][/i][color=#000000]they've attempted to solve the following problem for a few minutes. (There are various methods of solution to this problem.)[/color][br][br][b][color=#0000ff]Problem: [/color] [br][/b][color=#000000]Two ships ([/color][color=#ff0000]Ship A[/color][color=#000000] & [/color][color=#38761d]Ship B[/color][color=#000000]) are out at sea. [br][br][/color][color=#ff0000]Ship A[/color][color=#000000] 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 [/color][color=#ff0000]Ship A[/color][color=#000000] is at (50,100), [/color][color=#38761d]Ship B[/color][color=#000000] is at (900,250) and moves 4 feet west and 4 feet north every minute. [br][br]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. [br][br][b]Students: [br][/b]After interacting with the applet below for a few minutes, please answer the questions that follow. [/color]
[color=#0000ff][b]Questions:[/b][/color][br][br][color=#000000]Let [i]t[/i] = the time (in minutes) that pass since the start of this story. So, when [i]t[/i] = 0, [/color][color=#ff0000]point A[/color][color=#000000] is at (50,100) and [/color][color=#38761d]point B[/color][color=#000000] is at (900, 250). [br][br]1) Write a function that gives the x-coordinate of [/color][color=#ff0000]point [i]A[/i][/color][color=#000000] as a function of [/color][i]t[/i][color=#000000].[br][/color][color=#000000]2) [/color][color=#000000]Write a function that gives the y-coordinate of [/color][color=#ff0000]point [i]A[/i][/color][color=#000000] as a function of [/color][i]t[/i][color=#000000].[br][/color][color=#000000]3) [/color][color=#000000]Write a function that gives the x-coordinate of [/color][color=#38761d]point [i]B[/i][/color][color=#000000] as a function of [/color][i]t[/i][color=#000000].[br][/color][color=#000000]4) [/color][color=#000000]Write a function that gives the y-coordinate of [/color][color=#38761d]point [i]B[/i][/color][color=#000000] as a function of [/color][i]t[/i][color=#000000].[br][br]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. [/color]