A wind is blowing with a speed of 50 mph is a direction 40 degrees west of north. What is the westerly component of the wind's velocity? What is the northerly component of this velocity?
Vw = 50*sin40 = 32.14 mph.
Vn = 50*cos40 = 38.30 mph.
To find the westerly component and northerly component of the wind's velocity, you can use trigonometry and vector decomposition.
1. Start by drawing a diagram to represent the wind's velocity. Draw a reference line pointing north, and then draw an arrow representing the wind's velocity, making a 40-degree angle with the reference line.
2. Label the sides of the triangle formed by the wind's velocity arrow and the reference line as follows: The hypotenuse represents the magnitude of the wind's velocity (50 mph), the vertical side represents the northerly component (N), and the horizontal side represents the westerly component (W).
3. Use trigonometry to determine the values of the vertical and horizontal sides of the triangle. Since we have the magnitude of the hypotenuse and the angle, we can use the sine and cosine functions.
- The northerly component (N) can be calculated using the equation: N = hypotenuse * sin(angle)
N = 50 mph * sin(40 degrees)
- The westerly component (W) can be calculated using the equation: W = hypotenuse * cos(angle)
W = 50 mph * cos(40 degrees)
4. Calculate the values using a scientific calculator:
- N = 50 mph * sin(40 degrees) = 31.91 mph
- W = 50 mph * cos(40 degrees) = 38.29 mph
So, the westerly component of the wind's velocity is approximately 38.29 mph, and the northerly component of the velocity is approximately 31.91 mph.