Question 1208173: At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms, or 29.4 pounds per square inch.
(A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet).
(B) Interpret the slope of the model.
(C) Find the pressure at a depth of 80 ft.
(D) Find the depth at which the pressure is 6 atms.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch,
commonly referred to as 1 atmosphere of pressure. As an object descends in water, pressure P
and depth d are linearly related. In salt water, the pressure at a depth of 33 ft is 2 atms,
or 29.4 pounds per square inch.
(A) Find a linear model that relates pressure P (in pounds per square inch) to depth d (in feet).
(B) Interpret the slope of the model.
(C) Find the pressure at a depth of 80 ft.
(D) Find the depth at which the pressure is 6 atms.
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From the problem, when an object descents in water from the surface to the depth of 33 ft,
the pressure changes from 1 atm to 2 atm.
So, the rate of the pressure change is  =  atm/ft (atmosphere per foot of the depth).
Therefore, we can write the general formula for the pressure
P = 1 +  in atmospheres (1)
or
P = 14.7 +  in pounds per square inch, (2)
where d is the depth below the surface, in feet.
The last formula (2) is the answer to question (A), which is complete at this point.
In formula (2), the slope is the rate  = 0.4455 of a pound per foot of the depth
and per square inch of the surface area. It is the answer to question (B).
To answer (C), you should substitute d= 80 ft into formula (1) or (2) and make simple arithmetic.
From (1), you will get the pressure in atmospheres.
From (2), you will get the pressure in pounds per square inch.
To answer (D), you should solve this equation for d
14.7 + = 6*14.7.
You will get the answer in feet of the depth.
Happy calculations and happy solving !
You are fully instructed.
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In this problem, working units for pressure are atmosphere and pounds per square inch.
The problem and my solution teach you to work freely with different units of measurements.
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