Plane flying southwest at 155mi/hr. their is a wind from the west at 45.0mi/hr. what's the planes new velocity
To calculate the plane's new velocity, we need to consider the effect of the wind on the plane's motion.
Here's how you can calculate it:
1. Draw a diagram to represent the situation. Draw two vectors: one for the plane's velocity and one for the wind's velocity. The plane's velocity vector will be pointing southwest and have a magnitude of 155 mi/hr. The wind's velocity vector will be pointing directly from west to east and have a magnitude of 45.0 mi/hr.
2. Combine the plane's velocity vector and the wind's velocity vector. To do this, add the vectors together by placing them tip to tail. The resulting vector represents the plane's new velocity.
3. Use vector addition to calculate the new velocity. Since the plane is flying southwest and there is wind blowing from the west, the wind will affect the plane's velocity. To add the vectors, you can break them down into their x and y components.
The plane's velocity vector can be broken down into southwest components as follows:
Magnitude: 155 mi/hr
Component in the west direction: -155 * cos(45°) mi/hr (negative since it's southwest)
Component in the south direction: -155 * sin(45°) mi/hr (negative since it's southwest)
The wind's velocity vector is entirely in the east direction, so its components are:
Component in the west direction: 45.0 mi/hr
Component in the south direction: 0 mi/hr
4. Add the x-components (west direction) of the plane's velocity and the wind's velocity together:
-155 * cos(45°) mi/hr + 45.0 mi/hr
5. Add the y-components (south direction) of the plane's velocity and the wind's velocity together:
-155 * sin(45°) mi/hr + 0 mi/hr
6. Combine the x and y components to find the resultant vector. The resultant vector represents the plane's new velocity. Use the Pythagorean theorem to find the magnitude of the resultant vector, and use trigonometry to find its direction (angle):
New velocity magnitude: sqrt((combined x component)^2 + (combined y component)^2)
New velocity angle: atan((combined y component) / (combined x component))
By plugging the values into the formulas, you can find the magnitude and direction of the plane's new velocity with respect to the ground.