A Pilot Maintains heading due West With an airplane speed of 240 km/h the passengers was graduated from physics 20 measured the velocity of the aircraft relative to the ground and calculate it to be 180 km/h 35° north of West what is the magnitude and direction of the wind
To find the magnitude and direction of the wind, we can treat the velocity of the aircraft relative to the ground as the vector sum of the velocity of the airplane (240 km/h due West) and the velocity of the wind.
Let W be the velocity of the wind.
Let A be the velocity of the aircraft (240 km/h due West).
Let G be the velocity of the aircraft relative to the ground (180 km/h 35° north of West).
We can represent A and G as vectors:
A = 240 km/h due West = 240 km/h * <1, 0>
G = 180 km/h 35° north of West = 180 km/h * <cos(35°), sin(35°)>
We know that G = A + W, so:
180 km/h * <cos(35°), sin(35°)> = 240 km/h * <1, 0> + W
180 km/h * <cos(35°), sin(35°)> = 240 km/h * <1, 0> + <w1, w2>
This gives us two equations:
1. 180 * cos(35°) = 240 + w1
2. 180 * sin(35°) = w2
From equation 1, we get:
180 * cos(35°) - 240 = w1
w1 ≈ -107.974 km/h
From equation 2, we get:
180 * sin(35°) = w2
w2 ≈ 102.731 km/h
Therefore, the magnitude of the wind velocity is approximately sqrt(w1² + w2²) = sqrt((-107.974)² + (102.731)²) ≈ 153.34 km/h.
The direction of the wind can be found using the arctan function:
arctan(w2 / w1) = arctan(102.731 / -107.974) ≈ -41.03°
So, the wind velocity is approximately 153.34 km/h 41.03° south of West.