Airplane staring from airport a flies 300 km east then 395 km 26.5 degrees west of north, and then 150 km north to arrive at airport b. what angle is the straight flight from a to b north of east
and how far
Make the route plan
s₁= 300 =x₁+x₂
s₂ =395, α =26.5⁰
s₃ = 150
x₃ connects the point of s₂ and s₃ intersection and the point on s₁
which divides s₁ by x₁ and x₂ (x₃ ⊥ s₁)
s₄=? β =?
x₂ = s₂•sin α = 395 •sin 26.5 =176.25 km
x₃ =s₂•cos α = 395 •cos26.5 =353.5 km
s₃+ x₃ = 353.5+150 = 503.5 km
x₁ =s₁-x₂ =300-176.25 = 123.75 km
s₄ =sqrt{ (s₃+ x₃)²+x₁²} =
=sqrt(503.5²+123.75²) =518.5 km.
tan β = (s₃+ x₃)/x₁ =503.5/123.75 = 40.69
β = 88.6⁰
To find the angle between the straight flight from airport A to B, north of east, we can use trigonometry.
Let's break down the flight path:
1. The airplane flies 300 km east from airport A. This segment is a straight line and has no impact on the angle we are trying to find.
2. After flying east, the airplane flies 395 km 26.5 degrees west of north. This segment is in the northwest direction. To find the north component of this segment, we use the cosine function:
North component = 395 km * cos(26.5 degrees)
3. Finally, the airplane flies 150 km north to arrive at airport B. This segment is in the north direction and has no impact on the angle we are trying to find.
Now, let's calculate the north component of the second segment:
North component = 395 km * cos(26.5 degrees) ≈ 355.15 km
To find the angle between the straight flight from A to B and the east direction, we will use the tangent function. The east component is the initial 300 km east.
Tangent of the angle = North component / East component
Tangent of the angle = 355.15 km / 300 km
Now, let's calculate the angle:
Angle = atan(North component / East component)
Angle = atan(355.15 km / 300 km) ≈ 51.8 degrees
Therefore, the straight flight from airport A to B is approximately 51.8 degrees north of east.
As for the distance of the straight flight, we can calculate it by finding the magnitude of the total displacement. The displacement of the airplane is the vector sum of the east component, north component of the second segment, and the north component of the third segment.
Displacement = √(East component^2 + North component 2nd segment^2 + North component 3rd segment^2)
Displacement = √(300 km^2 + (355.15 km)^2 + (150 km)^2)
Now, let's calculate the distance:
Displacement = √(300 km^2 + (355.15 km)^2 + (150 km)^2) ≈ 497.2 km
Therefore, the distance of the straight flight from airport A to B is approximately 497.2 km.