Final answer:
The velocity of the wind with respect to the ground is determined using vector addition, considering the northward and westward components influenced by the wind velocity, which results in both magnitude and direction of the wind's velocity.
Step-by-step explanation:
The question involves solving for the wind velocity that affects an airplane's actual movement relative to the ground. To determine the wind's velocity, we use vector addition, since the airplane's speed and direction are influenced by the wind, altering the actual velocity observed.
Given that the airplane heads due north at a speed of 700 km/h and the actual velocity due to wind influence is 750 km/h at a 15° angle west of north, we can conclude the wind velocity has both a northward and westward component.
Using trigonometric functions and vector decomposition, we calculate the components of the wind's velocity. The northward component of the wind's velocity can be found by subtracting the airplane's speed due north from the northward component of the airplane's actual velocity. The westward component of the wind's velocity is the westward component of the airplane's actual velocity since there would be no westward speed without the wind. Finally, by combining these components, we can find the magnitude and direction of the wind's velocity.