As an object's depth below the surface of a body of salt water increases, so does the pressure acting on the object due to atmospheric and water conditions. The rate at which pressure increases is approximately 11 pounds per square inch (psi) for every increase in depth of 25 feet (ft). The pressure at the surface of the water is 15 psi. Rounded to the nearest foot, at what depth will the pressure acting on the object be 50 psi?

Question

As an object's depth below the surface of a body of salt water increases, so does the pressure acting on the object due to atmospheric and water conditions. The rate at which pressure increases is approximately 11 pounds per square inch (psi) for every increase in depth of 25 feet  (ft). The pressure at the surface of the water is 15 psi. Rounded to the nearest foot, at what depth will the pressure acting on the object be 50 psi?

Bytelearn · Accepted Answer

Calculate Additional Pressure: We know the pressure increases by 11 psi for every 25 ft increase in depth. The pressure at the surface is 15 psi. We want to find the depth at which the pressure is 50 psi. First, we calculate the additional pressure needed to reach 50 psi from the initial 15 psi. Additional pressure needed = Desired pressure - Initial pressureFind Number of Increments: Additional pressure needed = 50 psi - 15 psiRound to Nearest Whole Number: Additional pressure needed = 35 psi Now we need to find out how many increments of 11 psi are in 35 psi.Calculate Depth for 4 Increments: Number of increments = Additional pressure needed / Pressure increase per incrementFinal Depth Calculation: Number of increments = 35 psi / 11 psi per incrementNumber of increments = 3.1818... Since we can't have a fraction of an increment in this context, we need to round to the nearest whole number. However, since the pressure increases by 11 psi for each full increment of 25 ft, we need to find the number of full increments that will get us to at least 50 psi.The closest whole number of increments that will give us a pressure of at least 50 psi is 4 increments (since 3 increments would only give us 48 psi, which is less than 50 psi).Now we calculate the depth corresponding to 4 increments. Depth = Number of increments * Depth increase per incrementDepth = 4 increments * 25 ft per incrementDepth = 100 ft So, the depth at which the pressure acting on the object will be 50 psi, rounded to the nearest foot, is 100 feet.

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