# Direction of aeroplane query

• Sep 16th 2008, 12:02 PM
honeybumble
Direction of aeroplane query

An aeroplane flies in a straight line from city A (300, -200) to city B at (-100, 600).

(positions are given with reference to a Cartesian coordinate system whose x and y axes point due East and Due North respectively. Distance is in km.)

(1) Find the equation of the line'

I have m = rise/run = 800/-400 = -2

Then by applying equation y-y1 =m(x-x1) with m = -2 and (x1, y1) = (300, -200) I get:
y - (-200) = -2(x-300)

y = -2x + 400
(2) Find the direction of travel of the aeroplane, as a bearing, with the angle in degrees correct to one decimal place

I think I dont quite get this one...I've tried tan = -2 and get N 334.9 E

(3) Find the distance between cities A and B to the nearest km

Here I have done (-100-300)squared = (600-(-200))squared = 480000
Then apply the square root to this final figure get 693km

Then after landing at city B, the aeroplane flies in a straight line in the direction of S 23 W, to city C, before finally flying in a straight line in the direction of N 54 E back to city A.

(4) What is the distance between cities A and C, to the nearest km?

Please if any one could give me a few pointers I would be really grateful.

With regard to the aeroplane's flight from city A to city B. During this flight, it flies within range of an air traffic control centre at position (300,0)

(5) Find the parametric equations for the line of flight of the aeroplane. Your equations should be in terms of the parameter t , and should be such that the aeroplane is at city A when t = 0 and at city B when t= 1

This is what I have done.

The line of the slope is -2 and passes through (x1, y1) = (300, 0)

The parametric expressions are:

x = t + x1, y = mt + y1 leading to x = t + 300, y = -2t
(6) Write down an expression, in terms of t, for the square of the distance between the air traffic control centre and the aeroplane at the point with parameter t on the line of the flight of the aeroplane. Simplify your answer.

(the distance required here is the horizontal distance i.e. the distance between the air traffic control centre and the point on the ground immediately below the aeroplane.

(7) Using the answer to (6) above, and the method of completing the square, to determine the distance, to the nearest km, between the air traffic control centre and the aeroplane at the point on the line of flight of the aeroplane where it is closest to the air traffic control centre.

Many thanks
• Sep 16th 2008, 04:33 PM