Answer:
The component form of the velocity of the airplane is [tex]\vec v = 389.711\,\hat{i} -225\,\hat{j}\,\left[\frac{m}{s} \right][/tex].
Step-by-step explanation:
Let suppose that a bearing of 0 degrees corresponds with the [tex]+x[/tex] direction and that angle is measured counterclockwise. Besides, we must know both the magnitude of velocity ([tex]\|\vec v\|[/tex]), in miles per hour, and the direction of the airplane ([tex]\theta[/tex]), in sexagesimal degrees to construct the respective vector. The component form of the velocity of the airplane is equivalent to a vector in rectangular form with physical units, that is:
[tex]\vec v = \|\vec v\|\cdot (\cos \theta \,\hat{i}+\sin \theta\,\hat{j})[/tex] (1)
If we know that [tex]\|\vec v\| = 450\,\frac{mi}{h}[/tex] and [tex]\theta = 330^{\circ}[/tex], then the component form of the velocity of the airplane is:
[tex]\vec v = 389.711\,\hat{i} -225\,\hat{j}\,\left[\frac{m}{s} \right][/tex]
The component form of the velocity of the airplane is [tex]\vec v = 389.711\,\hat{i} -225\,\hat{j}\,\left[\frac{m}{s} \right][/tex].
