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 50 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 100 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. (Round your answers to one decimal place.)

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 50 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 100 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. (Round your answers to one decimal place.) true course N XE ground speed km/h

Answer 1

In order to find the magnitude of the resultant vector, we must find the components of the vector expressing the resultant. Then, the vector form representing the resultant velocity would be -

$\underset{v}{\rightarrow} = v_{x}\hat{i} + v_{y}\hat{j} + v_{z}\hat{k}$

In this problem the velocity is 2- Dimensional so last component (z) can be ignored.

$\underset{v}{\rightarrow} = v_{x}\hat{i} + v_{y}\hat{j}$

magnitude of the resultant would be -

$\left |\underset{v}{\rightarrow} \right | = \sqrt{v_{x}^{2}+v_{y}^{2}}$

and

$tan\Theta =\frac{v_{y}}{v_{x}}$

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vedos Direciou anolyeis - SoWsus" 100, 45° 60 50 su 45° 106 OS G0° Caloutaliow : - magnitede of velocity - (V) : Jaar.95)+ (1464)2 199 82 Km/hr. Ane. Thus, Cirouud Speed is 122-82 kmlhr. cau be found asiug- toue course The 29-65 14.644 tau 191.95 tan' (al20049) 6-845 The angle lee resultout makes wi pocilive ga aris Hhe 6.845° . is ite y- aris t forome. (90-68 45's = 83.155°. s0, the auswer is N 83-15°E Aus.