Positions are given with reference to a cartesian coordinate system

 In this question, positions are given with reference to a Cartesian coordinate system whose x- and y-axes point due East and due North, respectively. Distances are measured in kilometers.
A light aircraft travels at a constant speed of 480 kilometers per hour (kph) in a straight line from airport A, located at position (xA, yA) = (−200, 100), to airport B at (xB, yB) = (400,−100).
(a)
(i) Find the equation of the line of travel of the aircraft.
(ii) Find the direction of travel of the aircraft, as a bearing, with the angle in degrees correct to one decimal place.
(iii) Calculate the distance between airports A and B, in kilometers, correct to the nearest kilometer.
(iv) How long does the aircraft take to travel from A to B? Give your answer in hours and minutes, correct to the nearest minute.
(v) Find parametric equations for the line of travel of the aircraft. Your equations should be in terms of a parameter t, and should be such that the aircraft is at airport A when t = 0 and at airport B when t = 1.

Get a plagiarism free copy of this essay from our experts
Positions are given with reference to a cartesian coordinate system
Just from $13/Page
Order Now

(b) During its journey, the aircraft passes a landmark, L, located at position (90,−30).

(i) Let d kilometers be the distance between the location of the aircraft at parameter value t and the landmark L. Find an expression for d2 in terms of t. Simplify your result as far as possible.
(ii) Using your answer to part (b)(i) and the method of completing the square, determine the shortest distance, to the nearest kilometer, between the aircraft and the landmark L.
(iii) Landmark L is visible from a distance of at most 100 kilometers. Calculate the parameter values t1 and t2 when the landmark L can first and last be seen from the aircraft. For how many minutes is the landmark visible from the aircraft? 

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Order your essay today and save 15% with the discount code COCONUT