Been working on this question for a while. Have drawn a diagram (looks like a tilted trapezium, correct me if i'm wrong), but I still can't find any right angles to calculate the distance. Help would be appreciated, thanks.
Question:
A plane flies on a true bearing of 320° for 450 km. It then flies on a true bearing of 350° for 130 km and finally on a true bearing of 050° for 330 km. How far north of its starting point is the plane?
When using bearings, multiplying the distance by the Cos of the angle gives the vertical component instead of the usual hor. component. We need the vertical component only.
Displacement = 450km[320o] + 130[350o] + 330[50o].
Y = 450*Cos320 + 130*Cos350 + 330*Cos50 = 344.72 + 128.03 + 212.12 = 685 km, North.
ur mom
First of all you do not fly on a "bearing". You fly, or sail, on a "heading". A "bearing" is the direction a lighthouse or whatever is from you. Math texts are totally ignorant of navigation.
Anyway, let's do it in conventional x-y axes:
320 is 50 degrees above -x axis
so
in x y coordinates
x1 = -450 cos 50
y1 = +450 sin 50
350 is 80 degrees above -x axis
so
in x y coordinates
x2 = -130 cos 80
y2 = +130 sin 80
50 is 40 degrees above +x axis
so
in x y coordinates
x3 = 330 cos 40
y3 = 330 sin 40
NOW ADD those orthogonal (perpendicular to each other) vector components
x = x1 + x2 + x3
y = y1 + y2 + y3
north dist = y
no need to even calculate sqrt(x^2 + y^2) :)
Wow, you are really good at this, and also BIG thanks for the extremely quick reply and easy-to-understand solution <3
You are welcome :)
( I have spent some time at sea :)
To solve this question, you'll need to break it down into smaller steps. However, before we proceed, let's clarify a few things about the problem:
1. The true bearing is the angle between the direction of the plane's flight and the reference direction, which is usually the north direction.
2. The bearing is measured clockwise from the reference direction.
Now, let's break down the plane's journey into three steps:
Step 1: The plane flies on a true bearing of 320° for 450 km.
Step 2: The plane flies on a true bearing of 350° for 130 km.
Step 3: The plane flies on a true bearing of 050° for 330 km.
To find how far north of its starting point the plane is, we'll need to calculate the northward and eastward distances traveled separately and then use trigonometry to find the northward distance.
1. Step 1: To calculate the northward and eastward distances for Step 1, we'll use the cosine and sine functions, respectively, with the given true bearing and distance. Remember that the cosine of an angle gives the ratio of the adjacent side to the hypotenuse, while the sine gives the ratio of the opposite side to the hypotenuse.
Northward distance for Step 1 = 450 km * cos(320°)
Eastward distance for Step 1 = 450 km * sin(320°)
2. Step 2: Repeat the same process for Step 2.
Northward distance for Step 2 = 130 km * cos(350°)
Eastward distance for Step 2 = 130 km * sin(350°)
3. Step 3: Once again, repeat the process for Step 3.
Northward distance for Step 3 = 330 km * cos(50°)
Eastward distance for Step 3 = 330 km * sin(50°)
4. Finally, sum up the northward distances and subtract the eastward distances to find the total northward distance from the starting point.
Total northward distance = (Northward distance Step 1 + Northward distance Step 2 + Northward distance Step 3) - (Eastward distance Step 1 + Eastward distance Step 2 + Eastward distance Step 3)
Calculating these distances should give you the answer to how far north of its starting point the plane is located.