an aircraft heads north at 320km/h relative to the wind. the wind velocity is 80km/hr from the north. find the velocity of the aircraft relative to the ground.
Answers
velocity of aircraft is ...
320km/h - 80km/ h = 240 km/h
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Answer:
We need to use vector addition to find the aircraft's velocity relative to the ground. The aircraft's velocity relative to the ground can be obtained by adding the velocity of the aircraft relative to the wind and the velocity of the wind relative to the ground.
Explanation:
We are given that the aircraft is flying at a velocity of 320 km/h relative to the wind. Since the wind is blowing from the north with a velocity of 80 km/h, we can represent the velocity of the aircraft relative to the ground as:
The velocity of aircraft relative to ground = Velocity of aircraft relative to wind + Velocity of the wind relative to the ground
To obtain the magnitude of the aircraft's velocity relative to the ground, we need to calculate the vector sum of the velocities. Using the Pythagorean theorem, we can obtain the magnitude of the velocity of the aircraft relative to the ground as:
|Velocity of aircraft relative to ground| = √(320² + 80²) = √105600 = 325.27 km/h (approx.)
We can use trigonometry to determine the direction of the aircraft's velocity relative to the ground. The angle between the aircraft's velocity relative to the wind and the velocity of the aircraft relative to the ground is equal to the angle between the wind velocity and the ground, which is 90 degrees since the wind is blowing from the north. Therefore, the angle between the elicit of the aircraft relative to the ground and the north direction is given by:
θ = tan^(-1)(Velocity of aircraft relative to wind/Velocity of wind) = tan^(-1)(320/80) = 75.96 degrees (approx.)
Thus, the aircraft's velocity relative to the ground is 325.27 km/h, directed at an angle of 75.96 degrees north of the east direction.
To learn more about velocity, click on the given link.
https://brainly.in/question/36267867
To learn more about the wind, click on the given link.
https://brainly.in/question/27633367
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