Ship_Problem


 * Student Name:** Linda Fahlberg

** Statement of Problem: A ship is traveling at a constant speed from Port A. After 1 minute, it has gone 0.3mi east and 0.4 miles north. **
What do I need to do: Use the Rule of Four to completely describe this problem f**or 2 hours**. Questions: After 30 minutes, find its position relative to start, the distance it traveled and calculate its speed.

Rule 1: Description of variables with units, domain of x, rule for y Let **t= number of hours** Then t can have values: [0,2] Let x= distance in miles it has traveled EAST in t hours Let y= distance in miles it has traveled NORTH in t hour Then x=0.3 miles/minute *60 minutes/hour *t hours = 18t miles: **x=18t** and y=0.4 miles/minute *60 minutes/hour *t hours = 24t miles: **y=24t**

The distance traveled in t hours is math \,\,\,\,\,\, d = \sqrt{x^2+y^2} = \sqrt{(18t)^2+(24t)^2}=30t math

Rules 2-4: **GeoGebra worksheet with Algebra - Graph - Table** media type="custom" key="6639527"

Questions: After 1/2 hours, find its position relative to start, the distance it traveled and calculate its speed. Using the animation: We stop the animation and then use the Move tool to drag t=0.5. In Algebra View and in the Drawing pad, we see d=distance=15 miles and we see A=(9,12) In the spreadsheet, we see t=0.5, E=9, N=12 and D=15.

Calculating: a. x=18*0.5=36 so boat has traveled **9 miles east** of start b. y=24*0.5=12 so boat has traveled **12 miles north** of start. c. d=sqrt(9^2+12^2)=15 so boat has **traveled 15 miles** from start. d. The speed of the boat is d/t = 15/0.5 = **30 mph**.

Comments: **Use everything in Rule 1 in Rules 2-4.**
 * 1. Label all axes.**
 * 2. Use your relationship to calculate** all of the function and spreadsheet values.