Could use some help. I don't get this:
The maintenance department of a botanical garden is monitoring the displacement of statues that have moved by the process of creep. The statues must be straightened when the displacement reaches 15cm to prevent toppling. By measuring the tilt angle on the statues, they determined the creep rate in 2005 to be as shown in the table:
Date Installed...Rate (mm/yr)
1933.............2.01
1957.............2.35
1963.............3.1
1976.............2.69
1985.............2.5
Which statue will need to be straightened first?
To determine which statue will need to be straightened first, we need to calculate the displacement of each statue over time and compare them.
First, we need to convert the creep rate from millimeters per year (mm/yr) to centimeters per year (cm/yr) since the displacement is measured in centimeters.
Using the given creep rates:
1933: 2.01 mm/yr = 0.201 cm/yr
1957: 2.35 mm/yr = 0.235 cm/yr
1963: 3.1 mm/yr = 0.31 cm/yr
1976: 2.69 mm/yr = 0.269 cm/yr
1985: 2.5 mm/yr = 0.25 cm/yr
Now, we can calculate the displacement for each statue using the formula:
Displacement = Creep Rate * Time
Let's calculate the displacement for each statue:
For 1933 statue:
Displacement = 0.201 cm/yr * (2005 - 1933) yrs = 0.201 cm/yr * 72 yrs = 14.472 cm
For 1957 statue:
Displacement = 0.235 cm/yr * (2005 - 1957) yrs = 0.235 cm/yr * 48 yrs = 11.28 cm
For 1963 statue:
Displacement = 0.31 cm/yr * (2005 - 1963) yrs = 0.31 cm/yr * 42 yrs = 13.02 cm
For 1976 statue:
Displacement = 0.269 cm/yr * (2005 - 1976) yrs = 0.269 cm/yr * 29 yrs = 7.801 cm
For 1985 statue:
Displacement = 0.25 cm/yr * (2005 - 1985) yrs = 0.25 cm/yr * 20 yrs = 5 cm
Based on the calculations, the statue that will need to be straightened first is the one installed in 1976, as it has the highest displacement of 7.801 cm.