Construct Your Own Problem
Consider an airplane headed for a runway in a cross wind. Construct a problem in which you calculate the angle the airplane must fly relative to the air mass in order to have a velocity parallel to the runway. Among the things to consider are the direction of the runway, the wind speed and direction (its velocity) and the speed of the plane relative to the air mass. Also calculate the speed of the airplane relative to the ground. Discuss any last minute maneuvers the pilot might have to perform in order for the plane to land with its wheels pointing straight down the runway.
The plane is flying in a cross wind. This means the plane has a path perpendicular to the wind direction. Let us assume that the plane is flying toward the runway at a velocity of 200 m/s due west and the wind has a velocity of 40 m/s due north. We are required to calculate the angle the the airplane should fly to have a velocity parallel to the runaway. We are also required to calculate the velocity of the plane with respect to air and the ground.
Step 1 of 3</p>
Let us simplify the situation with the figure below.
If the plane flies due west the wind direction will make it follow a path away from the runway. Therefore, to fly parallel to the runway, the plane has to fly at at angle relative to the mass. This angle can be calculated as shown below.
The wind moves due north with a velocity 40 m/s.
The plane flies due west with a velocity of 200 m/s.
Therefore, the angle
Therefore, the plane has to fly making an angle of due south of west with respect to the air mass so that it can continue to fly parallel to the runway.
Step 2 of 3</p>
Along the flight direction, the plane has a velocity component of
The velocity component of the air mass along the direction of the plane’s flight is
But this velocity would be in a direction opposite to that of the plane’s velocity.
Hence the velocity of the plane with respect to the ground is m/s
The approximate velocity of the plane with respect to the ground will be 188.2 m/s.