What direction should the plane head to end up going due east?
The plane should head in the direction determined by the angle between the eastward component of the airspeed and the resultant velocity.
Explanation:
To determine the direction the plane should head to end up going due east, we need to find the resultant velocity vector. The airspeed of the plane is 510 km/hr, and the wind is blowing at 55 km/hr toward the southeast.
First, we need to break down the airspeed and wind velocity into their respective components. The airspeed can be broken down into an eastward component and a northward component. Since the plane is heading due east, the eastward component of the airspeed is 510 km/hr. The wind velocity can be broken down into a southeastward component and a northward component. The southeastward component of the wind velocity is 55 km/hr.
Next, we can find the resultant velocity by adding the respective components of the airspeed and wind velocity. The eastward component of the resultant velocity is the sum of the eastward component of the airspeed and the southeastward component of the wind velocity. The northward component of the resultant velocity is the sum of the northward component of the airspeed and the northward component of the wind velocity.
Using trigonometry, we can find the direction of the resultant velocity. The angle between the eastward component and the resultant velocity can be found using the inverse tangent function. This angle represents the direction the plane should head to end up going due east.