When you scuba dive, the added pressure due to the water varies directly with your depth. At 20 feet, the added pressure is about 9 pounds per square inch.
a) If an amateur diver can safely stand an added pressure of 30 (psi), how deep could he dive?
b) A sunken submarine lies in 120 feet of water. How much added pressure would a diver experience in going to the submarine?
To answer these questions, we need to use the concept of direct variation and apply it to the given information.
a) Let's start by setting up a proportion to find the maximum depth the amateur diver can safely dive.
The added pressure varies directly with depth, so we can set up the proportion as follows:
Added pressure at 20 feet / Depth at 20 feet = Added pressure the diver can withstand / Maximum depth the diver can reach
Using the given information, we have:
9 psi / 20 ft = 30 psi / x
Cross-multiplying and solving for x, we get:
(9 psi)(x) = (20 ft)(30 psi)
9x = 600
x = 600 / 9
x ≈ 66.67 ft
Therefore, the amateur diver can safely dive to a depth of approximately 66.67 feet.
b) To calculate the added pressure experienced by a diver going to a depth of 120 feet, we can set up another proportion using the given information.
Added pressure at 20 feet / Depth at 20 feet = Added pressure at 120 feet / Depth at 120 feet
Using the given information, we have:
9 psi / 20 ft = x psi / 120 ft
Cross-multiplying and solving for x, we get:
(9 psi)(120 ft) = (20 ft)(x psi)
1080 psi-ft = 20x psi-ft
x = 1080 psi-ft / 20 ft
x = 54 psi
Therefore, a diver would experience an added pressure of 54 psi when going to a depth of 120 feet.