Use the given flight data to compute the ground speed, the drift angle, and the course (round your answers to two decimal places). The heading and air speed are 45^(@) and 275mph, respectively, the wind is 50mph from 135^(@).

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Vector Addition Explanation: To solve this problem, we will use vector addition to combine the velocity vector of the aircraft with the wind vector to find the resulting ground speed and direction. The aircraft's velocity vector is 275 mph at a heading of 45 degrees. The wind's velocity vector is 50 mph from 135 degrees, which means it is blowing towards the southwest. We will convert these headings into standard mathematical angles measured counterclockwise from the positive x-axis. Aircraft heading angle: 45 degrees (no conversion needed as it is already in the standard mathematical direction). Wind angle: 135 degrees is equivalent to 180 - 135 = 45 degrees measured clockwise from the negative x-axis.Convert Headings: Next, we will break down the aircraft's velocity and the wind's velocity into their respective components along the x (east-west) and y (north-south) axes. Aircraft velocity components: Vx (aircraft) = 275 mph * cos(45 degrees) Vy (aircraft) = 275 mph * sin(45 degrees) Wind velocity components: Vx (wind) = 50 mph * cos(45 degrees) (since the wind is from 135 degrees, this component will be negative) Vy (wind) = 50 mph * sin(45 degrees) (since the wind is from 135 degrees, this component will also be negative)Calculate Components: Now we will calculate the components. Vx (aircraft) = 275 mph * cos(45 degrees) = 275 mph * (sqrt(2)/2) ≈ 194.66 mph Vy (aircraft) = 275 mph * sin(45 degrees) = 275 mph * (sqrt(2)/2) ≈ 194.66 mph Vx (wind) = -50 mph * cos(45 degrees) = -50 mph * (sqrt(2)/2) ≈ -35.36 mph Vy (wind) = -50 mph * sin(45 degrees) = -50 mph * (sqrt(2)/2) ≈ -35.36 mphAdd Velocity Components: We will now add the components of the aircraft's velocity and the wind's velocity to find the ground speed components. Vx (ground) = Vx (aircraft) + Vx (wind) = 194.66 mph - 35.36 mph ≈ 159.30 mph Vy (ground) = Vy (aircraft) + Vy (wind) = 194.66 mph - 35.36 mph ≈ 159.30 mphCalculate Ground Speed: The ground speed magnitude can be found by calculating the resultant vector's magnitude using the Pythagorean theorem. Ground speed = sqrt((Vx (ground))^2 + (Vy (ground))^2) Ground speed = sqrt((159.30 mph)^2 + (159.30 mph)^2)Find Drift Angle: Calculating the ground speed magnitude: Ground speed = sqrt((159.30 mph)^2 + (159.30 mph)^2) = sqrt(2 * (159.30 mph)^2) = 159.30 mph * sqrt(2) ≈ 225.35 mphCalculate Course: To find the drift angle, we need to calculate the angle of the ground speed vector relative to the aircraft's heading. This can be done using the arctan function to find the angle between the resultant ground speed vector and the positive x-axis, and then adjusting for the aircraft's initial heading. Drift angle = arctan(Vy (ground) / Vx (ground)) - aircraft heading Drift angle = arctan(159.30 mph / 159.30 mph) - 45 degreesCalculating the drift angle: Drift angle = arctan(159.30 mph / 159.30 mph) - 45 degrees = arctan(1) - 45 degrees = 45 degrees - 45 degrees = 0 degrees The drift angle is 0 degrees, which means there is no drift, and the aircraft's course is the same as its heading.Finally, we will calculate the course. Since the drift angle is 0 degrees, the course is the same as the heading. Course = aircraft heading + drift angle Course = 45 degrees + 0 degrees = 45 degrees

Use the given flight data to compute the ground speed, the drift angle, and the course (round your answers to two decimal places). The heading and air speed are $45^{\circ}$ and $275 \mathrm{mph}$ , respectively, the wind is $50 \mathrm{mph}$ from $135^{\circ}$ .

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