Final answer:
Using the Pythagorean theorem, the resulting velocity of the airplane relative to the ground, considering the northward velocity of 100 km/h and westward wind at 30 km/h, is approximately 104.48 kilometers per hour.
Step-by-step explanation:
To find the velocity of an airplane traveling north at 100 kilometers per hour with a crosswind blowing west at 30 kilometers per hour, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, the airplane's northward velocity and wind's westward velocity form the two perpendicular components of the triangle.
Let's denote Vn as the northward velocity of the airplane (100 km/h), Vw as the westward velocity of the wind (30 km/h), and Vr as the resulting velocity of the airplane relative to the ground.
Using the Pythagorean theorem:
- Vr2 = Vn2 + Vw2
- Vr2 = (100 km/h)2 + (30 km/h)2
- Vr2 = 10000 + 900
- Vr2 = 10900
- Vr = √10900
- Vr = 104.48 km/h
The resulting velocity (Vr) of the airplane relative to the ground is approximately 104.48 kilometers per hour.