3) A wind with a speed of 60 km/h is directed TOWARDS the SE. A plane, flying due NORTH has an airspeed of 280 m/s. What is the speed (in compass notation) the plane is actually travelling as seen by an air traffic controller on the ground?
241 @ N10E
To calculate the speed of the plane as seen by the air traffic controller on the ground, we need to consider the effect of the wind on its movement. We can break down the problem into two components: the northward or southward component of the wind, and the eastward or westward component of the wind.
Let's start by calculating the eastward or westward component of the wind:
Given that the wind speed is 60 km/h, we can break it down into its eastward and westward components using trigonometry. Since the wind is directed towards the southeast, we can consider it as an angle of 45 degrees with respect to the east.
Using the cosine function, we can find the westward component of the wind:
Westward component = wind speed * cosine of the angle
Westward component = 60 km/h * cos(45°)
Next, let's calculate the northward or southward component of the wind:
Using the sine function, we can find the northward component of the wind:
Northward component = wind speed * sine of the angle
Northward component = 60 km/h * sin(45°)
Now, let's determine the effect of the wind on the plane's airspeed:
The plane's airspeed is given as 280 m/s, which represents its speed without any external factors like wind. To find its actual speed, we need to subtract the wind's components from the airspeed in the respective directions.
For the northward or southward direction, we subtract the northward component of the wind:
Actual speed in the northward direction = Airspeed - Northward component of wind
For the eastward or westward direction, we subtract the westward component of the wind:
Actual speed in the eastward direction = Airspeed - Westward component of wind
Since the plane is flying due north, the actual speed in the eastward direction can be considered negligible. Therefore, the actual speed of the plane as seen by the air traffic controller on the ground is the same as its actual speed in the northward direction.
After calculating the actual speed in the northward direction, we can express it in compass notation by replacing the negative sign with the letter "S" to indicate a southward direction.
By following these steps, you can calculate the speed (in compass notation) at which the plane is actually traveling as seen by the air traffic controller on the ground.