An airplane pilot tries to fly directly east with a velocity of 800.0 km/h. If wind comes from the southwest at 80.0 km/h, what is the relative velocity of the airplane to the surface of Earth?
Well, if the airplane pilot tries to fly directly east with a velocity of 800.0 km/h and the wind comes from the southwest at 80.0 km/h, I'm afraid the airplane might end up doing some sort of sideways shuffle, like a penguin trying to dance the tango.
But to calculate the relative velocity, we need to take into account both the velocity of the airplane and the velocity of the wind. So let's crunch some numbers, shall we?
Since the wind is coming from the southwest, we can break it down into its horizontal and vertical components. The horizontal component would be 80.0 km/h, and the vertical component... well, let's not get into that, shall we? We're trying to fly here, not do acrobatics!
Now, to determine the relative velocity, we simply subtract the wind velocity from the airplane velocity. So, 800.0 km/h minus 80.0 km/h gives us... *drumroll*... 720.0 km/h!
So, the relative velocity of the airplane to the surface of the Earth would be 720.0 km/h. But remember, this is all just relative. In reality, the airplane might still be waltzing with the wind.
To determine the relative velocity of the airplane to the surface of the Earth, we need to consider the vector addition of the airplane's velocity and the wind velocity.
Given:
Airplane velocity = 800.0 km/h (directly east)
Wind velocity = 80.0 km/h (from the southwest)
To simplify the problem, we can break down the wind velocity into its northward and eastward components.
The southwest direction is a combination of south and west directions. To find the northward component of the wind velocity:
Northward component of the wind velocity = wind velocity × sin(45°)
= 80.0 km/h × sin(45°)
= 80.0 km/h × √2 / 2
= 40.0 km/h × √2
To find the eastward component of the wind velocity:
Eastward component of the wind velocity = wind velocity × cos(45°)
= 80.0 km/h × cos(45°)
= 80.0 km/h × √2 / 2
= 40.0 km/h × √2
Now, let's add the northward and eastward components of the wind velocity to the airplane's velocity to find the relative velocity of the airplane to the surface of the Earth.
Northward component of relative velocity = 0 km/h (since the airplane is flying directly east)
Eastward component of relative velocity = airplane velocity - eastward component of wind velocity
= 800.0 km/h - (40.0 km/h × √2)
Therefore, the relative velocity of the airplane to the surface of the Earth is:
√((Northward component of relative velocity)^2 + (Eastward component of relative velocity)^2)
Note: The northward component of the relative velocity is 0 km/h since the airplane is flying directly east, so the remaining computation simplifies to just the eastward component of the relative velocity.
Relative velocity = √((40.0 km/h × √2)^2) = √((40.0 × √2)^2) = √(1600 × 2) = √3200 ≈ 56.57 km/h
Therefore, the relative velocity of the airplane to the surface of the Earth is approximately 56.57 km/h in the eastward direction.
To find the relative velocity of the airplane to the surface of the Earth, we need to consider the horizontal components of both the airplane's velocity and the wind's velocity separately and then combine them.
Let's break down the given information:
- The airplane is flying directly east with a velocity of 800.0 km/h.
- The wind is coming from the southwest, indicating a direction opposite to the eastward flight of the airplane, with a velocity of 80.0 km/h.
To calculate the relative velocity, we'll apply vector addition.
Step 1: Break down the given velocities into their horizontal components.
- The airplane's velocity is 800.0 km/h directly east. The horizontal component of this velocity is 800.0 km/h.
- The wind's velocity is 80.0 km/h, oriented southwest. To calculate the horizontal component, we need to find the component of the velocity in the eastward direction. Since southwest is 45 degrees between south and west, the horizontal component can be found using trigonometry: cos(45) = adjacent/hypotenuse = horizontal component/wind velocity.
horizontal component = wind velocity * cos(45) = 80.0 km/h * cos(45) = approximately 56.6 km/h.
Step 2: Combine the horizontal components.
To find the relative velocity, we add the horizontal components of the airplane and the wind. Since they are in opposite directions, we subtract the horizontal component of the wind from the airplane's horizontal component.
relative velocity = 800.0 km/h - 56.6 km/h = approximately 743.4 km/h.
Therefore, the relative velocity of the airplane to the surface of the Earth is approximately 743.4 km/h, directed eastward.
Break up the SW wind into N and E,
and add.
the wind is blowing towards 80Cos45E+80Sin45N