Beaufort Scale and Wind Effects
0 Smoke rises vertically
1 Smoke shows wind direction
2 Wind felt on face
3 Leaves move, flags extend
4 Paper, small branches move
5 Small trees sway, flags beat
6 Large branches sway, flags beat
7 Large branches sway, walking is difficult
8 Twigs break, walking is hindered
9 Slight roof damage
10 Severe damage, trees uprooted
11 Widespread damage
12 Devastation
The Beaufort scale was devised by Frances Beaufort in 1805 to measure wind speeds. The scale is numbered from 0 to 12, and represents wind speeds in the open, 33 feet above ground. The Beaufort scale, B, can be modeled by the function
b=1.9�ã(x+8-5.4)
where x is the speed of the wind in miles per hour.
Sketch the graph of this function.
To sketch the graph of the function b = 1.9(x + 8 - 5.4), which represents the Beaufort scale, we need to understand how the graph behaves and plot some key points.
1. Start by simplifying the equation:
b = 1.9(x + 2.6)
Distribute the 1.9 to both terms inside the parentheses:
b = 1.9x + 3.34
2. Now we can plot some points. Since the Beaufort scale measures wind speeds from 0 to 12, we'll choose some values within that range and calculate the corresponding b values.
- Let's choose x = 0: b = 1.9(0) + 3.34 = 3.34
- Let's choose x = 6: b = 1.9(6) + 3.34 = 15.14
- Let's choose x = 12: b = 1.9(12) + 3.34 = 25.94
Plot these points on a graph, with the x-axis representing wind speed (x) and the y-axis representing the Beaufort scale (b).
Point 1: (0, 3.34)
Point 2: (6, 15.14)
Point 3: (12, 25.94)
3. Draw a line passing through these points. Since the function is linear, the graph will be a straight line.
Start from Point 1, and draw a straight line that passes through Points 2 and 3.
/\
/ \
/ \
/ \
/_________\
This is a rough sketch of the graph of the function b = 1.9(x + 8 - 5.4), representing the Beaufort scale.