What is the speed over the ground of an airplane flying at 100 km/h relative to the air with a 100 km/h right-angle crosswind?

To determine the speed over the ground of an airplane flying at 100 km/h relative to the air with a 100 km/h right-angle crosswind, we can use the Pythagorean theorem. The airplane's speed relative to the air and the wind speed can be thought of as forming two sides of a right triangle, where the airplane's airspeed is one side and the crosswind speed is the other side.

In this scenario, one side of the triangle (the airplane's speed) is 100 km/h, while the other side (the wind speed) is also 100 km/h. To find the resultant speed over the ground (the hypotenuse of the triangle), we calculate it as follows:

1. Square the speed of the airplane: (100^2 = 10,000)
2. Square the speed of the wind: (100^2 = 10,000)
3. Add these two values together: (10,000 + 10,000 = 20,000)
4. Take the square root of the sum to find the hypotenuse: (\sqrt{20,000} \approx 141.42) km/h.

Thus, the speed of the