Final answer:
The plane's resultant velocity is found by vector addition of the northward and eastward components, resulting in 111.8 m/s at 26.57 degrees east of north, which does not match any of the provided options.
This correct answer is none of the above.
Step-by-step explanation:
The question involves finding the resultant velocity of a plane that is affected by wind, which is a common problem in physics relating to vectors.
To solve this, we treat the plane's velocity and the wind's velocity as vectors and use vector addition. The plane's velocity vector is 100 m/s due north and the wind's velocity vector is 50 m/s due east. We can use the Pythagorean theorem to calculate the magnitude of the resultant vector:
\(\sqrt{(100 m/s)^2 + (50 m/s)^2} = \sqrt{10000 + 2500} = \sqrt{12500} = 111.8 m/s\)
Next, we calculate the angle using the inverse tangent function, where the angle \(\theta\) is the angle east of north:
\(\theta = \tan^{-1}(\frac{50}{100}) = 26.57^\circ\)
So the plane's resultant velocity is 111.8 m/s at 26.57 degrees east of north. None of the provided options match this correct result.
This correct answer is none of the above.