Due to a strong wind from the west of 65 km/h, a plane ends up traveling 330 km/h [W 15 S] relative to the ground. What was the magnitude of the velocity of the plane relative to the air in km/h?
330 cos 15 = Vwest - 65
330 sin 15 = Vsouth
so
Vwest = 383.7 km/h
Vsouth = 85.4 km/hr
Vplane = sqrt (383.7^2+85.4*2)
tan angle south of west = 85.4/383.7
To find the magnitude of the velocity of the plane relative to the air, we need to subtract the effect of the wind from the ground speed of the plane.
Let's break down the information given in the question:
- The ground speed of the plane is 330 km/h [W 15 S], which means it is moving westward with a heading of 15 degrees southward from due west.
- The wind is blowing from the west at a speed of 65 km/h.
To calculate the magnitude of the velocity of the plane relative to the air, we can use vector addition. We'll consider the plane's velocity relative to the ground as one vector and the wind's velocity as another vector, both acting in the same direction.
First, let's find the northward and eastward components of the plane's ground speed. We can use trigonometry:
Northward component = 330 km/h * sin(15°)
Eastward component = 330 km/h * cos(15°)
Next, let's consider the wind's effect. Since the wind is blowing from the west, it will have a negative effect on the eastward speed of the plane:
Northward component of wind = 0 km/h * sin(180°)
Eastward component of wind = -65 km/h * cos(0°)
Now, we can add the northward and eastward components of the plane's ground speed and the wind's velocity to get the total northward and eastward components of the plane's velocity relative to the air:
Total northward component = Northward component + Northward component of wind
Total eastward component = Eastward component + Eastward component of wind
Finally, we can use the Pythagorean theorem to find the magnitude of the velocity:
Magnitude of velocity = sqrt((Total northward component)^2 + (Total eastward component)^2)
By plugging in the values and calculating, you should get the magnitude of the velocity of the plane relative to the air in km/h.