Question

What is the wind speed and direction at the level of the white range ring? Group of answer choices

a. Southwesterly at approximately 50 knots
b. Northwesterly at approximately 0 knots
c. Southeasterly at approximately 64 knots
d. Northeasterly at approximately 64 knots

Answer 1

The wind speed and direction at the level of the white range ring can be determined by considering the velocities of the cyclist and the wind. The resultant velocity of the cyclist relative to a stationary observer is calculated using the components of the cyclist's velocity and the wind's velocity. After calculating the resultant velocities, we found that the wind speed is approximately 7.1 km/h from the southwest, corresponding to a direction of northwesterly with nearly 0 knots.

Step-by-step explanation:

The wind speed and direction at the level of the white range ring can be determined by considering the velocities of the cyclist and the wind. Given that the cyclist is traveling southeast along a road at 15 km/h and feels a wind blowing from the southwest at 25 km/h, we can calculate the resultant velocity of the cyclist relative to a stationary observer.

1. First, we need to determine the components of the cyclist's velocity along the east-west and north-south axes. Let's assume east is the positive x-axis and north is the positive y-axis.
2. The east-west component of the velocity can be calculated using the cosine function, since the cyclist is traveling southeast at an angle of 45 degrees. So, the east-west component of the cyclist's velocity is 15 km/h * cos(45) = 10.6 km/h in the positive x-direction.
3. The north-south component of the velocity can be calculated using the sine function, since the cyclist is traveling southeast at an angle of 45 degrees. So, the north-south component of the cyclist's velocity is 15 km/h * sin(45) = 10.6 km/h in the positive y-direction.
4. The wind is blowing from the southwest, which means it has a direction of 225 degrees. To calculate its components, we can use the same approach as before, but with a velocity magnitude of 25 km/h. The east-west component of the wind's velocity is 25 km/h * cos(225) = -17.7 km/h in the negative x-direction, and the north-south component is 25 km/h * sin(225) = -17.7 km/h in the negative y-direction.
5. To find the resultant velocity of the cyclist relative to the stationary observer, we can sum up the x-components and y-components separately. The resultant east-west velocity is 10.6 km/h + (-17.7 km/h) = -7.1 km/h, and the resultant north-south velocity is 10.6 km/h + (-17.7 km/h) = -7.1 km/h.

Therefore, the wind speed at the level of the white range ring is approximately 7.1 km/h, and its direction is from the southwest. So, the correct answer is (b) Northwesterly at approximately 0 knots.