Respuesta :
Answer:
v_air = 118.10 km / h , θ = 36 º (36 north east)
Explanation:
In this exercise we can look for air velocity, the easiest method is to decompose the speed in a reference system, we used trigonometry
d = 135 km
θ= 45.0 south-east
This Angle measured from the positive side of the x-axis is
θ = 360-45
θ = 315º
sin 315 = y / d
cos 315 = x / d
y = d sin315
x = d cos 315
y = 135 sin 315 = -95.46 km
x = 135 cos 315 = 95.46 km
Airplane distance after 1 hour
D₁ = v / t =
D₁ = 165/1 = 165 km
[tex]D_{1y}[/tex] = -165 j ^
D₁ₓ = 0 i^
Total distance traveled
D₁ₓ = x - x_air
D_{1y} = y - y_air
x_air = x -D₁ₓ
y_air = y -D_{1y}
x_air = 95.46 - 0
x_air = 95.46 km
y_air = -95.46 - (-165)
y_air = 69.54 km
As the air has a constant speed we can use the speed formula
v = d / t
vₓ = x / t
vₓ = 95.46 km / h
[tex]v_{y}[/tex] = 69.54 km / h
To give the module let's use Pythagoras
v_air = √ (vₓ² + v_{y}²)
v_air = √ (95.46² + 69.54²)
v_air = 118.10 km / h
For the direction let's use trigonometry
tan θ = v_{y} / vₓ
θ = tan⁻¹ v_{y} / vₓ
θ = tan⁻¹ 69.54 / 95.46
θ = 36 º
In cardinal notation is 36 north east
Answer:
The speed of the wind is 118.10km/h in the direction 36.07° north of east.
Question:
A light plane is headed due south with a speed relative to still air of 165 km/h . After 1.00 h, the pilot notices that they have covered only 135 km and their direction is not south but southeast 45.0. What is the wind velocity?
Explanation:
Resultant distance moved by the plane = distance moved by plane in still air + distance moved as a result of wind.
R = Dp + Dw
Dp = speed of plane in still air × time of travel = 165km/h × 1 h = 165km south
R = 135km South east
Resolving the distance to x and y components.
Let north represent positive y component and east represent positive x component.
x- component
135cosθ = 0 + Dwx
Dwx = 135cos45 = 95.46km
y- component
-135sinθ = -165 + Dwy
Dwy = 165 - 135sin45
Dwy = 69.54 km
Dw = √(95.46^2 + 69.54^2)
Dw = 118.10 km
Speed = distance/time = 118.10km/1h = 118.10km/h
Angle
Tanθ = Dwy/Dwx = 69.54/95.46
θ = taninverse(69.54/95.46)
θ = 36.07°
Since both x and y component are positive (north and east)
The speed of the wind is 118.10km/h in the direction 36.07° north of east.
