Answer :
Final answer:
To find the plane's resultant velocity, subtract the wind's velocity from the plane's velocity due to their opposite directions. The magnitude of the plane's resultant velocity is 35 mph, and its direction is due north.
Explanation:
To determine the plane's resultant velocity, we need to take into account the velocity of the plane and the velocity of the wind. The plane is flying due north at 2.00 x 10 mph, while the wind blows due south at 45 mph.
To find the resultant velocity, we can use vector addition. Since the velocity of the plane and the velocity of the wind are in opposite directions, we subtract the magnitude of the wind's velocity from the magnitude of the plane's velocity. This gives us:
|v_resultant| = |v_plane| - |v_wind| = 2.00 x 10 mph - 45 mph = 2.00 x 10 - 45 mph = -35 mph
Here, the negative sign indicates that the resultant velocity is in the opposite direction of the plane's velocity. Therefore, the magnitude of the plane's resultant velocity is 35 mph, and its direction is due north.
Learn more about plane's resultant velocity here:
https://brainly.com/question/33318976
Final answer:
The plane's resultant velocity would be 155 mph due north after subtracting the southward wind speed from the plane's northward speed.
Explanation:
The question is asking to determine the resultant velocity of an airplane when it experiences a wind blowing in the opposite direction to its motion. When a plane flies due north at a certain speed and encounters a wind blowing due south, we subtract the wind speed from the plane's speed to find the resultant velocity, since the directions are opposite.
In this case, we are given that a plane is flying due north at 200 mph and encounters a wind blowing due south at 45 mph. The resultant velocity can be calculated by subtracting the wind speed from the plane's speed:
Resultant velocity = Plane's speed - Wind's speed
Therefore:
Resultant velocity = 200 mph - 45 mph = 155 mph
The resultant velocity is therefore 155 mph, and since the plane's speed is still greater than the wind's speed, the plane continues to fly north, which is the direction of the resultant velocity.
