An airplane is flying North with a velocity of 22 m/s. A strong wind is blowing East at 50 m/s. What is the airplane's resultant velocity (magnitude and direction)?
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To find the resultant velocity of the airplane, we need to apply vector addition. The airplane is moving in the North direction with a velocity of 22 m/s, and the wind is blowing in the East direction with a velocity of 50 m/s. Since the wind velocity is perpendicular to the airplane's velocity, we can use the Pythagorean theorem to find the magnitude of the resultant velocity.
To find the magnitude, we square the velocity components, add them, and then take the square root of the sum:
Magnitude = √(22^2 + 50^2)
= √(484 + 2500)
= √2984
≈ 54.63 m/s
The direction of the resultant velocity can be determined by finding the angle between the resultant velocity and the North direction. We can use the inverse tangent (arctan) function to find this angle:
Direction = arctan(50/22)
≈ 66.35°
Therefore, the airplane's resultant velocity is approximately 54.63 m/s in a direction of 66.35° East of North.