Question

When you go swimming the pressure in your ears varies directly with the depth at which you swim. At 10 feet, the pressure is about 4.3 pounds per square inch (psi). a) Write the variation function. b) Predict the pressure at 50 feet. c) It is unsafe for amateur divers to swim where the pressure is more than 65 psi. How deep can an amateur swimmer safely swim (round to the nearest thousandth)

Answer 1

(a)
`p = 0.43d`

(b)
`p = 21.5`

(c)
`d = 151.163`

Explanation:

Given

Variation: Direct

Represent ear pressure with p and depth with d.

So, we have:

`p\ \alpha\ d`

`d =10` when
`p =4.3`

Solving (a): Write a variation

We have:

`p\ \alpha\ d`

Write as an equation

`p = kd`

Where: k is the constant of variation

`d =10` when
`p =4.3`

So, we have:

`4.3 = k * 10`

Make k the subject

`k = (4.3)/(10)`

`k = 0.43`

Substitute 0.43 for k in
`p = kd`

`p = 0.43d`

Solving (b): Pressure at 50 feet

Substitute 50 for d in
`p = 0.43d`

`p = 0.43 * 50`

`p = 21.5`

The pressure is 21.5 pounds per square

Solving (c): The safe depth

The safe depth stops at a pressure of 65psi.

Substitute 65 for p in
`p = 0.43d`

`65 = 0.43 * d`

Make d the subject

`d = (65)/(0.43)`

`d = 151.162790698`

`d = 151.163` -- approximated

The safe distance for an amateur is 151.163ft