Application Giovanni is flying his Cessna airplane on a heading as shown. His instrument panel shows an air speed of 130 mi/h. (Air speed is the speed in still air without wind.) However, there is a 20 mi/h crosswind. What is the resulting speed of the plane?
sqrt (130^2 + 20^2)
To find the resulting speed of the plane, considering the crosswind, we can use vector addition. The air speed of 130 mi/h is the speed of the plane in still air, and the crosswind of 20 mi/h affects the plane's movement perpendicular to its heading.
Using the Pythagorean Theorem, we can determine the resulting speed, which is the hypotenuse of a right triangle formed by the air speed and the crosswind.
Let's use Vair for air speed (130 mi/h), Vcross for crosswind (20 mi/h), and Vresultant for the resulting speed we need to find.
The equation will be:
Vresultant^2 = Vair^2 + Vcross^2
Substituting the given values:
Vresultant^2 = 130^2 + 20^2
Vresultant^2 = 16900 + 400
Vresultant^2 = 17300
Taking the square root of both sides:
Vresultant = sqrt(17300)
Vresultant ≈ 131.5 mi/h
Therefore, the resulting speed of the plane, considering the crosswind, is approximately 131.5 mi/h.