Final answer:
The maximum depth under water a human could theoretically survive is approximately 100 feet, assuming their body can take a maximum pressure of 58 psi and factoring in the incremental pressure increase of 0.433 psi per foot of depth.
Step-by-step explanation:
The question asks for the maximum depth under water a human could survive, given that the human body can withstand a pressure of 58 psi (pounds per square inch). To find the answer, we first understand that at sea level, the atmospheric pressure is about 14.7 psi. The pressure due to water increases by an additional 0.433 psi for every foot of depth due to the weight of the water above. To calculate the maximum depth, we can set up the following equation:
Total pressure = atmospheric pressure + (pressure per foot of depth × depth)
Since we want the total pressure to be equal to the maximum pressure the human body can take (58 psi), we can rearrange the equation to solve for the depth:
58 psi = 14.7 psi + (0.433 psi/foot × depth)
We can then subtract the atmospheric pressure from both sides and solve for the depth:
58 psi - 14.7 psi = (0.433 psi/foot × depth)
43.3 psi = (0.433 psi/foot × depth)
Finally, dividing both sides by the pressure per foot gives us the depth:
Depth = 43.3 psi / 0.433 psi/foot
Depth ≈ 100 feet (rounded to the nearest foot)
This implies that the maximum depth under water a human could survive without being crushed by the pressure is approximately 100 feet.