Question

A diver experiences a pressure of 8517 pounds per square foot at a certain depth. Given that the pressure increases at a rate of 64 pounds per square foot for each foot the diver descends and the pressure at the surface of the water is 2117 pounds per square foot, what is the depth at which the diver is located?

a) 10 feet
b) 120 feet
c) 125 feet
d) 130 feet

Answer 1

To determine the diver's depth, subtract the surface pressure from the total pressure to find the pressure increase due to water, then divide by the pressure increase rate per foot. My calculation resulted in a depth of 100 feet, which does not match any of the given answer choices.

Step-by-step explanation:

The problem involves determining the depth at which a diver is located based on the water pressure experienced. Given the pressure at the surface (2117 pounds per square foot) and the rate at which pressure increases with depth (64 pounds per square foot per foot descended), the student can set up a linear equation to solve for the depth:

Depth pressure = Surface pressure + (Pressure increase per foot × Number of feet descended)

Start by subtracting the surface pressure from the depth pressure to find the total pressure increase due to water alone:

8517 lb/ft² (depth pressure) - 2117 lb/ft² (surface pressure) = 6400 lb/ft² (pressure increase due to water)

Then, divide by the pressure increase per foot to find the depth:

6400 lb/ft² / 64 lb/ft² per foot = 100 feet

Therefore, the diver is at a depth of 100 feet, which is not one of the given options, and it seems like there might be a discrepancy in the question or the answer choices.