a jet airliner, flying initially 300 mi/hr due east, suddenly enters a region where the wind is blowing 100…

Explanation:

Step1: Resolve wind - velocity components

The wind velocity $\vec{v}w = 100$ mi/hr at $30^{\circ}$ north of east. The east - west component of the wind velocity $v{wx}=100\cos30^{\circ}$ and the north - south component $v_{wy}=100\sin30^{\circ}$. $v_{wx}=100\times\frac{\sqrt{3}}{2}=50\sqrt{3}$ mi/hr, $v_{wy}=100\times\frac{1}{2} = 50$ mi/hr. The initial velocity of the airliner $\vec{v}_a=300$ mi/hr due east.

Step2: Calculate the resultant east - west and north - south components of velocity

The resultant east - west component of velocity $v_x=300 + 50\sqrt{3}$ mi/hr and the resultant north - south component of velocity $v_y = 50$ mi/hr.

Step3: Use the Pythagorean theorem to find the resultant speed

The resultant speed $v=\sqrt{v_x^{2}+v_y^{2}}$. $v_x=300 + 50\sqrt{3}\approx300+50\times1.732=300 + 86.6=386.6$ mi/hr, $v_y = 50$ mi/hr. $v=\sqrt{(386.6)^{2}+50^{2}}=\sqrt{149459.56 + 2500}=\sqrt{151959.56}\approx389.8$ mi/hr.

Answer:

Approximately $390$ mi/hr