Question

An airplane is heading due south at a speed of 620 km/h . A wind begins blowing from the southwest at a speed of 105 km/h (average).
In what direction should the pilot aim the plane so that it will fly due south?

Answer 1

Answer on Question #85202 - Physics - Mechanics | Relativity

An airplane is heading due south at a speed of $620~\mathrm{km / h}$ . A wind begins blowing from the southwest at a speed of $105~\mathrm{km / h}$ (average).

In what direction should the pilot aim the plane so that it will fly due south?

Solution:

Figure out the velocity triangle (not to scale):

On this figure:

$\overrightarrow{AB}$ - the vector of the airplane's air speed;

$\overrightarrow{BC}$ - the vector of the wind's speed;

$\overrightarrow{AC}$ - the vector of the airplane's ground speed, that equals a vector sum of air speed and wind speed vectors.

In the additional rectangular triangle BDC the angle CBD equals $45{}^{\circ}$ , because wind blows from southwest.

So from the rectangular triangle ADB we get

$$\psi = \arcsin \left(\frac {B D}{A B}\right).$$

From the rectangular triangle BDC we get

$$B D = B C \cdot c o s 4 5 {}^ {\circ}.$$

So

$$\psi = \arcsin \left(\frac {BC \cdot \cos 45{}^{\circ}}{AB}\right) = \arcsin \left(\frac {105 \cdot 0.707}{620}\right) = 6.88{}^{\circ}.$$

The angle of the aircraft heading, measured from the direction of the north, will be equal to $180{}^{\circ} \psi$, that is $186.88{}^{\circ}$.

Answer: The angle of the aircraft heading, measured from the direction of the north, will be equal to $186.88{}^{\circ}$.

Answer provided by https://www.AssignmentExpert.com