Math Problem Statement

The water pressure on a submerged object is given by p=64d, where p is the pressure in pounds per square foot, and d in the object's depth in feet. Find the depth of a submerged object if the pressure is 672 pounds per square foot.

Solution

To find the depth dd of a submerged object given the pressure pp, we can use the formula:

p=64dp = 64d

Given that p=672p = 672 pounds per square foot, substitute this value into the equation:

672=64d672 = 64d

Now, solve for dd by dividing both sides of the equation by 64:

d=67264d = \frac{672}{64}

d=10.5 feetd = 10.5 \text{ feet}

So, the depth of the submerged object is 10.5 feet.

Would you like further details or clarifications? Here are some related questions to consider:

  1. How does pressure change with depth in general?
  2. What factors influence water pressure apart from depth?
  3. How can we calculate pressure in different liquids?
  4. What is the relationship between pressure and force in fluids?
  5. How does the density of the fluid affect pressure calculations?

Tip: Always ensure units are consistent when working with formulas. This avoids common calculation errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Physics

Formulas

p = 64d

Theorems

Linear equation solution

Suitable Grade Level

Grades 6-8