Final answer:
The speed of the wind is 3 mph.
Step-by-step explanation:
To find the speed of the wind, we need to use vector addition. First, we need to break down the velocity of the airplane into its horizontal and vertical components. Since the airplane is flying to the east, the horizontal component of its velocity is 100 mph. The southern wind pushes the plane off course by 15 degrees, so we can use trigonometry to find the vertical component of the airplane's velocity. Given that the magnitude of the velocity is 100 mph, we can use the sine and cosine of 15 degrees to find the vertical component:
Vertical component = 100 mph * sin(15) = 25.80 mph
Next, we can use vector addition to find the velocity of the airplane relative to the earth. The horizontal component remains the same at 100 mph, but the vertical component changes to 25.80 mph due to the wind:
Velocity relative to the earth = sqrt((100 mph)^2 + (25.80 mph)^2) = 103 mph
Therefore, the speed of the wind is 103 mph - 100 mph = 3 mph.