To be considered safe for ocean sailing, the capsize screening value C should be less than 2.  For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the...

To be considered safe for ocean sailing, the capsize screening value C should be less than 2.  For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function

            C = 4d - 1/3b

1. What is the capsize screening value of a boat which has a displacement of 23,245 pounds and a beam of 13.5 feet?

2.  Solve the formula for d.

3.  For what displacement is the boat safe for ocean sailing? (b = 13.5)

Please explain the steps of the solutions.

Asked on by gturner49

2 Answers | Add Yours

caledon's profile pic

caledon | High School Teacher | (Level 3) Senior Educator

Posted on

Please note that the formula is incorrect as shown; a required value of C<2 with this formula would produce unrealistic results, such as a 100 pound boat needing to be over 1000 feet wide.

Please check your data to ensure that the formula is correct. My research suggests the correct formula is;

C = 4(d^(-1/3)) x b

1. This is simply a matter of plugging the given values into the given equation.

C = 4(d^(-1/3)) x b

d = 23,245

b = 13.5

4(23,245^(-1/3))13.5

C = 1.89

2. To solve for D:

C = 4b(d^-1/3)

Isolate d on one side of the equation

C/4b = d^-1/3

Eliminate the exponent. Recall that raising an exponent to another exponent is the same as multiplying them together. We'll multiply -1/3 by another exponent so that it equals 1.

-1/3 x 3 = 1

(C/4b)^-3 = D

3. The maximum safe displacement is:

2 = 4(d^-1/3)b

2 = 4(d^-1/3)13.5

2=54(d^-1/3)

(2/54) = d^-1/3

(2/54)^3 = 19683

The displacement must be less than 19683 pounds.

Again, please be sure that the equation you're using is correct.

gturner49's profile pic

gturner49 | (Level 1) Honors

Posted on

Thank you.  Yes, there was an error in the formula which I found out after submitting the question.  Thank you for your assistance.

Gloria

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