Final answer:
The ground speed of an airplane flying at 100 km/h in a 100 km/h crosswind is calculated using Pythagoras' theorem, resulting in approximately 141.42 km/h.
Step-by-step explanation:
The question concerns the ground speed of an airplane that is attempting to fly with a 100 km/h crosswind. To solve for this, we typically use vector addition because wind speed affects the plane's resultant velocity relative to the ground. Since the wind is a crosswind, it blows perpendicular to the direction of the plane's motion. The airplane's speed and the wind speed form a right angle. This can be illustrated using Pythagoras' theorem in a right-angled triangle, where the plane's airspeed and the wind speed are the two sides, and the ground speed is the hypotenuse.
Using the Pythagorean theorem, if we let c be the ground speed, a be the plane's airspeed, and b be the wind speed, we have c^2 = a^2 + b^2. Given a = 100 km/h and b = 100 km/h, then:
c^2 = (100 km/h)^2 + (100 km/h)^2
c^2 = 10,000 km^2/h^2 + 10,000 km^2/h^2
c^2 = 20,000 km^2/h^2
c = √20,000 km^2/h^2
c = 141.42 km/h
Therefore, the ground speed of the airplane is approximately 141.42 km/h.