A women, flying her plane south at 398 km/h when she encounters a wind blowing west at 104 km/h...
A)...what would her resulting velocity be if she made no course correction
B)...what speed and direction should she change to in order to maintain her original velocity.
Thanks for your help
check your previous post.
A. Vr = -104 - 398i = 411.4km/h[75.4o]
S. of W. = 14.6o W. of S.
B. 411.4km/h[14.6o] E. of S.
To find the resulting velocity in each scenario, we can use vector addition by breaking down the velocities into their horizontal and vertical components.
Let's start with scenario A, where the pilot makes no course correction. We have a plane flying south at 398 km/h and a wind blowing west at 104 km/h.
A) Resulting Velocity with No Course Correction:
To find the resulting velocity, we need to add the velocity of the plane and the velocity of the wind. However, since they are moving in different directions, we need to consider them as vectors.
The horizontal component of the resulting velocity will be the sum of the horizontal components of the plane's velocity and the wind's velocity.
Horizontal Component: 0 km/h (Plane) + (-104 km/h) (Wind) = -104 km/h
The vertical component of the resulting velocity will be the sum of the vertical components of the plane's velocity and the wind's velocity.
Vertical Component: (-398 km/h) (Plane) + 0 km/h (Wind) = -398 km/h
Therefore, the resulting velocity with no course correction would be (-104 km/h) west and (-398 km/h) south.
B) Speed and Direction for Maintaining Original Velocity:
To maintain her original velocity, the pilot needs to adjust her course so that her resultant velocity is equal in magnitude but opposite in direction to the original velocity.
To find the required speed and direction of the course adjustment, we need to subtract the velocity of the wind from the original velocity.
The horizontal component of the required speed and direction will be the difference between the horizontal component of the plane's velocity and the wind's velocity.
Horizontal Component: 0 km/h (Plane) - (-104 km/h) (Wind) = 104 km/h
The vertical component of the required speed and direction will be the difference between the vertical component of the plane's velocity and the wind's velocity.
Vertical Component: (-398 km/h) (Plane) - 0 km/h (Wind) = -398 km/h
Therefore, the required speed and direction to maintain the original velocity would be 104 km/h west and 398 km/h south.