The magnitude of a velocity vector is called speed. Suppose that a wind is blowi

Question

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 30 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 150 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. Give your answers correct to one decimal place.

Explanation / Answer

Alright so from the equation we have that:

xwind =30*cos(45)=21.213 ywind = 30*sin(45)=21.213 Xground=150cos(60)=75 Yground=150sin(60)=129.9038

Because the wind is 45 degrees off north in the west direction, we will be adding the y directional speeds, while subtracking the x directional speed. So we get

Xair = 75-30cos(45)=53.786 Yair = 150sin(60)+30sin(45)=151.117

This gives us a total air speed of 160.4037762 km/h, or ground speed as you mention it

For the true course we need to use the law of sins:

so we have

160.4037762/sin(45)=30/sin(x). solving for x results in 7.5995 or 7.6 degrees off north in the eastern direction.

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