Parametric Equations (I)
Here's a PDF of the problem below.
[b][color=#0000ff]Problem: [/color] [br][/b][color=#000000]Two ships ([/color][color=#ff0000][b]Ship A[/b][/color][color=#000000] & [/color][color=#38761d][b]Ship B[/b][/color][color=#000000]) are out at sea. [br][br][/color][color=#ff0000][b]Ship A[/b][/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][b]Ship A[/b][/color][color=#000000] is at (50,100), [/color][color=#38761d][b]Ship B[/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 app below for a few minutes, please answer the questions that follow. [/color]
[size=150][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][b]point [i]A[/i][/b][/color][color=#000000] is at (50,100). [br][br][/color][color=#000000]Write a function that gives the [b]x-coordinate [/b]of [/color][color=#ff0000][b]point [i]A [/i][/b][/color][color=#000000]as a function of [/color][i]t[/i][color=#000000].[br][/color]Then w[color=#000000]rite a function that gives the y[b]-coordinate [/b]of [/color][color=#ff0000][b]point [i]A[/i] [/b][/color][color=#000000]as a function of [/color][i]t[/i][color=#000000].[/color][/size]
[size=150][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=#38761d][b]point [i]B [/i][/b][/color][color=#000000][i]i[/i]s at (900, 250). [br][br][/color][color=#000000]Write a function that gives the [b]x-coordinate [/b]of [/color][b][color=#38761d]point [/color][i][color=#38761d]A[/color][/i][/b][color=#000000]as a function of [/color][i]t[/i][color=#000000].[br][/color]Then w[color=#000000]rite a function that gives the y[b]-coordinate [/b]of [/color][b][color=#38761d]point [i]B [/i][/color][/b][color=#000000]as a function of [/color][i]t[/i][color=#000000].[/color][/size]
[size=150]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. [/size]