A plane is flying southwest at 155 mi/h and encounters a wind from the west at 45.0 mi/h. What is the plane's velocity in respect to the ground in standard position?
I know the answer, but can't figure out how to get the answer. Any help would be appreciated!
V = 155mi/h @ 225o + 45mi/h @ 0o.
X = 155*cos225 + 45 = -64.6 Mi/h.
Y = 155*sin225 = -109.6 Mi/h.
V^2 = X^2 + Y^2.
V^2 = (-64.6)^2 + (-109.6)^2 = 16,185.66
V = 127.2 Mi/h.
To find the plane's velocity in respect to the ground, we need to apply vector addition. Let's break down the given information:
1. The plane is flying southwest at 155 mi/h.
2. The wind is coming from the west at 45.0 mi/h.
We can represent the plane's velocity as a vector pointing in the southwest direction with a magnitude of 155 mi/h.
Now, let's consider the wind. It is coming from the west, which means its velocity is directly opposite to the east direction. So, we can represent the wind's velocity as a vector pointing in the east direction with a magnitude of 45.0 mi/h.
To find the plane's velocity in respect to the ground, we simply need to combine the plane's velocity vector and the wind's velocity vector using vector addition.
To do this, we can graphically represent the vectors on a coordinate system, or we can break down the vectors into their x and y components. Let's use the component method:
1. We can represent the southwest direction as a combination of south and west directions. Assuming south is the positive y-axis direction and west is the negative x-axis direction, the plane's velocity vector in component form can be represented as (-155√2, -155√2).
2. The wind is coming from the west, which means it has a velocity of -45.0 mi/h in the x-axis direction. Therefore, the wind's velocity vector in component form can be represented as (-45.0, 0).
Now, we can simply add the respective components of the plane's velocity vector and the wind's velocity vector:
(-155√2, -155√2) + (-45.0, 0) = (-155√2 - 45.0, -155√2)
The result gives us the resultant vector of the plane's velocity in respect to the ground. By calculating the magnitude and the direction of this resulting vector, we can determine the plane's velocity in respect to the ground in standard position.