An aircraft pilot wishes to fly from an airfield to a point lying S20oE from the airfield. There is a wind blowing from N80oE at 45 km/h. The airspeed of the plane will be 550 km/h.
(a) What direction should the pilot steer the plane (to whole degree)? Include a diagram as part of your solution.
(b) What will the actual ground speed be of the plane (to one decimal place)?
can someone show me step by step??
see the first Similar Question below
steve what did the diagram look like? did they both start from the origin? or were they head to tail??? and was the wind going N80E or S80W off the first vector??
a. TYPO: Remove the -24.5.
Of course! Let's break down the problem step by step.
Step 1: Determine the components of wind velocity
The wind velocity is given as 45 km/h at a direction of N80oE. To find the components, we need to split it into its northward (N) and eastward (E) components using trigonometry.
The northward component (Vn) is given by:
Vn = wind velocity * sin(wind angle)
Vn = 45 km/h * sin(80o)
Vn ≈ 44.47 km/h (rounded to two decimal places)
The eastward component (Ve) is given by:
Ve = wind velocity * cos(wind angle)
Ve = 45 km/h * cos(80o)
Ve ≈ 9.11 km/h (rounded to two decimal places)
Step 2: Determine the true airspeed (TAS)
The true airspeed is the speed of the aircraft relative to the air around it. It is given as 550 km/h.
TAS = 550 km/h
Step 3: Determine the ground speed (GS)
The ground speed is the speed of the aircraft relative to the ground.
To find the ground speed, we need to combine the true airspeed and the components of wind velocity. We will use vector addition to find the resultant ground speed.
The northern component (N) of the ground speed is given by:
N = Vn
N ≈ 44.47 km/h (rounded to two decimal places)
The eastern component (E) of the ground speed is given by:
E = TAS + Ve
E ≈ 550 km/h + 9.11 km/h (rounded to two decimal places)
E ≈ 559.11 km/h (rounded to two decimal places)
To find the magnitude of the ground speed (GS) and its direction (θ), we use the Pythagorean theorem and trigonometry:
GS = √(N^2 + E^2)
θ = arctan(N / E)
GS = √(44.47^2 + 559.11^2)
θ = arctan(44.47 / 559.11)
GS ≈ 561.45 km/h (rounded to two decimal places)
θ ≈ 4.54o (rounded to two decimal places)
Step 4: Determine the direction the pilot should steer the plane
The direction the pilot should steer the plane is the direction of the ground speed. By convention, we measure direction clockwise from the north. In this case, the direction will be an angle from north (N).
Direction = 360o - θ (to whole degree)
Direction = 360o - 4.54o
Direction ≈ 355o (rounded to whole degree)
So, to summarize:
(a) The pilot should steer the plane in the direction of 355o.
(b) The actual ground speed of the plane will be approximately 561.45 km/h.
S20oE = 160o CW.
The Wind Blowing
From : 80o E. of N.
Heading: 80o W. of S. = 260o CW.
a. -24.5o]Vp + Vw = 550km/h[160o].
Vp + 45[260o] = 550[160],
Vp + 45*sin260 + i45*Cos260 = 550*sin160 + i550*Cos160,
Vp + (-44.3) + (-7.81i) = 188.1 + (-516.8i),
Vp = 232.4 - 509i = 559.5[-25o] = 559.5km/h[25o] E. of S.
arcTanA(X/Y). A = 25o.
b. Ground speed = 559.5 km/h.
vp + Vw =