>
#mathematics
,
#aeronautics
,
#physics
>
An airplane is flying in the direction of 43°east of north also abbreviated as N43E at a speed of 550m/h.Awind with speed 25m/h comes from the south west at a bearing of NISE.What is the ground speed?
Anonymous
Mar 7
An airplane is flying in the direction of 43°east of north also abbreviated as N43E at a speed of 550m/h.Awind with speed 25m/h comes from the south west at a bearing of NISE.What is the ground speed?
1 view
1 view
1 answer
Sort By
ChatGPT
Mar 7
To find the ground speed, we need to calculate the resultant velocity of the airplane by considering both its velocity and the wind velocity.
First, we need to break down the velocity of the airplane into its northward and eastward components. Using trigonometry, we can find:
Northward component = 550 * sin(43°) = 550 * 0.6819 ≈ 375.5 m/h
Eastward component = 550 * cos(43°) = 550 * 0.7314 ≈ 402.3 m/h
Next, we need to break down the wind velocity into its northward and eastward components. Since the wind is coming from the southwest at a bearing of NISE, it is blowing in the northward direction. Therefore, the northward component of the wind velocity is 25 m/h.
Now, we can find the resultant velocity of the airplane by adding the northward and eastward components of both the airplane's velocity and the wind velocity:
Resultant northward velocity = 375.5 + 25 = 400.5 m/h
Resultant eastward velocity = 402.3
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √(400.5^2 + 402.3^2) ≈ 568.6 m/h
Therefore, the ground speed of the airplane is approximately 568.6 m/h.
First, we need to break down the velocity of the airplane into its northward and eastward components. Using trigonometry, we can find:
Northward component = 550 * sin(43°) = 550 * 0.6819 ≈ 375.5 m/h
Eastward component = 550 * cos(43°) = 550 * 0.7314 ≈ 402.3 m/h
Next, we need to break down the wind velocity into its northward and eastward components. Since the wind is coming from the southwest at a bearing of NISE, it is blowing in the northward direction. Therefore, the northward component of the wind velocity is 25 m/h.
Now, we can find the resultant velocity of the airplane by adding the northward and eastward components of both the airplane's velocity and the wind velocity:
Resultant northward velocity = 375.5 + 25 = 400.5 m/h
Resultant eastward velocity = 402.3
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity:
Resultant velocity = √(400.5^2 + 402.3^2) ≈ 568.6 m/h
Therefore, the ground speed of the airplane is approximately 568.6 m/h.
1
