SOLUTION: Word Problem Create a mch Find the matart vector in each problem and direction 1. An airplane is flying 340 km/hr at 12° North of Pan. The wind is blowing 40 km at 34° South o

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Question 1204112: Word Problem Create a mch Find the matart vector in each problem and direction
1. An airplane is flying 340 km/hr at 12° North of Pan. The wind is blowing 40 km at 34° South of East What is the plane actual velocity?
Answer by asinus(45) About Me  (Show Source):
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**1. Define the Coordinate System**
* Let's define our coordinate system with:
* **East as the positive x-axis**
* **North as the positive y-axis**
**2. Resolve the Velocities into Components**
* **Plane's Velocity:**
* Magnitude: 340 km/hr
* Direction: 12° North of East
* x-component: 340 * cos(12°) = 332.54 km/hr (East)
* y-component: 340 * sin(12°) = 70.43 km/hr (North)
* **Wind Velocity:**
* Magnitude: 40 km/hr
* Direction: 34° South of East
* x-component: 40 * cos(34°) = 33.14 km/hr (East)
* y-component: -40 * sin(34°) = -22.36 km/hr (South)
**3. Calculate the Resultant Velocity**
* **Resultant x-component:** 332.54 km/hr (plane) + 33.14 km/hr (wind) = 365.68 km/hr
* **Resultant y-component:** 70.43 km/hr (plane) - 22.36 km/hr (wind) = 48.07 km/hr
**4. Calculate the Magnitude of the Resultant Velocity**
* Magnitude = √(x-component² + y-component²)
* Magnitude = √(365.68² + 48.07²)
* Magnitude ≈ 369.45 km/hr
**5. Calculate the Direction of the Resultant Velocity**
* Direction = arctan(y-component / x-component)
* Direction = arctan(48.07 / 365.68)
* Direction ≈ 7.48° North of East
**Therefore:**
* **Magnitude of the plane's actual velocity:** 369.45 km/hr
* **Direction of the plane's actual velocity:** 7.48° North of East
**In summary:**
The plane's actual velocity is 369.45 km/hr at a direction of 7.48° North of East, taking into account the effect of the wind.