To fly east while accounting for the northward wind, the plane must point slightly to the north of east. This is because the wind will push the plane off course towards the north.
To determine the exact direction the plane must point, we can use vector addition. Let's consider the velocity of the plane in still air as the eastward component and the wind velocity as the northward component.
The magnitude of the eastward component is 280 km/h, and the magnitude of the northward wind component is 60 km/h.
Using vector addition, we can find the resultant velocity (total velocity) of the plane. The direction of the resultant velocity will be the direction the plane must point to fly exactly east.
To find the magnitude of the resultant velocity, we can use the Pythagorean theorem. The resultant velocity can be calculated as:
Resultant velocity = √(280^2 + 60^2) = √(78400 + 3600) = √82000 ≈ 286.48 km/h
So, the total velocity of the plane would be approximately 286.48 km/h.
To find the direction the plane must point, we can use trigonometry.
The angle between the eastward component and the resultant velocity can be calculated as:
θ = tan^(-1)(60/280) ≈ 12.14°
Therefore, the plane must point approximately 12.14° north of east to fly exactly east in the presence of the northward wind.
Hope this helped ;)