a plane is flying due north at 155 mi/h and encounters a wind from the west at 45m/h. what is the plane's new velocity with respect to the ground in standard position.
answer is 128 mi/h at 239.4. how do i get to this answer.
a plane is flying southwest at 155 mi/h and encounters a wind from the west at 45m/h. what is the plane's new velocity with respect to the ground in standard position.
answer is 128 mi/h at 239.4. how do i get to this answer.
To find the plane's new velocity with respect to the ground, we can use vector addition. The velocity of the plane will have two components: the velocity due to its own motion (due north at 155 mi/h) and the velocity due to the wind (from the west at 45 mi/h).
1. Convert the velocity components into vector form:
- The velocity due to the plane's own motion can be represented as (0, 155) mi/h.
- The velocity due to the wind can be represented as (-45, 0) mi/h since it is from the west and there is no component in the north-south direction.
2. Add the two vectors together to find the resultant velocity:
- To add the vectors, simply add their corresponding components. In this case, add the x-components and the y-components separately.
- (0 + (-45), 155 + 0) = (-45, 155) mi/h
3. Find the magnitude and direction of the resultant velocity:
- The magnitude of the resultant velocity can be calculated using the Pythagorean theorem: √((-45)^2 + 155^2) = √(2025 + 24025) = √26050 ≈ 161.35 mi/h.
- The direction can be found using trigonometry. Since the resultant velocity has a negative x-component and a positive y-component, the angle will be in the second quadrant. The inverse tangent of the y-component divided by the x-component gives the angle: arctan(155/-45) ≈ -74.22 degrees.
- Convert the angle to the standard position by adding 180 degrees to get 180 - 74.22 ≈ 105.78 degrees.
Therefore, the plane's new velocity with respect to the ground is approximately 161.35 mi/h at 105.78 degrees (measured counterclockwise from the positive x-axis).
I do not agree with that answer. You should add 155 N and 45 W as vectors.
I get a ground speed of 161.4 mph, with a direction 16.2 degrees West of North.