the table shows the wind pressure on a structure at different heights in pa. using linear interpolation, estimate the pressure at a height of 17 ft. 6 in
the table is below:
height(ft) pressure(pa)
13 254
14 269
15 278
16 287
17 296
18 311
19 319
20 326
height = 13, 14, 15, 16, 17, 18, 19
pressure = 254, 269, 278, 287, 296, 311, 319, 326
17'6" is halfway between 17' and 18'
So, pick a pressure value halfway between 296 and 311
That's what linear interpolation is all about.
To estimate the pressure at a height of 17 ft 6 in, we can use linear interpolation. Linear interpolation is a method to estimate values within a set of given data points by drawing a straight line between two adjacent points.
First, let's convert the height of 17 ft 6 in to a decimal. Since there are 12 inches in a foot, the height can be calculated as:
17 ft + (6 in / 12) = 17.5 ft
Now, let's locate the two data points that surround the height of 17.5 ft. In this case, the closest points are:
Height(ft) Pressure(pa)
17 296
18 311
We can use these data points to perform the linear interpolation.
Linear interpolation formula:
Pressure at 17.5 ft = Pressure at 17 ft + (Height difference * Pressure difference)
Pressure difference = Pressure at 18 ft - Pressure at 17 ft
= 311 - 296
= 15 pa
Height difference = 17.5 ft - 17 ft
= 0.5 ft
Now, let's substitute these values into the formula:
Pressure at 17.5 ft = 296 + (0.5 * 15)
= 296 + 7.5
= 303.5 pa
Therefore, using linear interpolation, the estimated pressure at a height of 17 ft 6 in is approximately 303.5 pa.