Well this is my Portfolio Problem:

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I am flying my 1958 Cessna 172, Starting at Heathrow Airport in London, England and I head North East along the baring 70ยบ degrees and moving at a steady rate of 102 mph.

1. What are the Parametric equations for the line I am on?
I travel to the point (95.87, 34.9) in one hour (t)
y=34.9(t)
x=95.87(t)

2. What is the standard form equation of the line I am on?

Sitmo_Standard_Form_Equation_Portfolio_#1.png

3. When will I be over ocean rather than land and where is this point?

The cross over is at (68.81, 25.05) and it took me 43.07 minutes to fly there, and I am 73.22 miles away from London.

Land_over_Sea.PNG

I solved this by creating a triangle with sides of 68.81, 25.05, and x.
I then used the Pythagriam Theorm to find the length of the Hypotenuse (x).
Sitmo_Equation_Portfolio_Problem_pt_1.png
Sitmo_Equation_Portfolio_Problem_pt_2.png
Sitmo_Equation_Portfolio_Problem_pt_3.png
Then I did the following to convert it into time:
Sitmo_Equation_for_time_1.png
=43.07 minutes

4. If I increased my speed from 102 mph to 110 mph how much sooner would I reach the Sea?
Sitmo_Equation_for_time_2.png
=39.93 minutes

5. At what point would I be closest to Rotterdam?
Rotterdam_to_line.PNG

I found this answer by creating a parallel flight path that goes through Rotterdam. Then I took the perpendicular bisector of that line on the point Rotterdam, which gives me a strait line between Rotterdam and my flight path.
Then I found the intersection point at: (179.41, 65.31) where I will be the closest to Rotterdam.

6. At what point am eqidistant between Den Haag and Norwich?
I took the following steps to find this:
1) Created a line segment between Norwich and Den Haag.
2) Found the midpoint on that line.
3) Created a perpendicular bisector of the line segmant on point H
4) Found the intersection point between the perpendicular bisector and my flight path.
(124.94, 45.48)

Mid_point_between_Nowich_and_Den_Haag.PNG

7. If I am flying at the point (172.87, 62.93) and I notice that I only have 8 gallons left of fuel. My plane only gets 5 miles to the gallon. Which of the following Airports will I be able to land at and how long will it take me
to get there?
I found that I can reach any airport within a 40 mile radius by:
Sitmo_Equation_Portfolio_Problem_fuel_1.png
Sitmo_Equation_Portfolio_Problem_fuel_2.png

I found the time it takes to fle there by the equation:
Sitmo_Equation_Portfolio_Problem_fuel_time_1.png

Zaanstad: 33.51 miles away: reachable: 19.71 minutes
Haarlemmermeer: 31.35 miles away: reachable: 18.44 minutes
Den Haag: 28.28 miles away: reachable: 16.63 minutes
Utrecht: 51.97 miles away: unreachable: 30.57 minutes
Rotterdam: 39.98 miles away: reachable: 23.51 minutes
Amersfoort: 59.54 miles away: unreachable: 35.02 minutes
Leiden: 28.87 miles away: reachable: 16.98 minutes
Amersterdam: 36.93 miles away: reachable: 21.72 minutes
Almere: 49.97 miles away: unreachable: 29.39 minutes

Portfolio_Fuel_Problem.PNG




Heathrow Airport: