Question 164708
The maximum hull speed, S, is directly proportional to the square root of the length of the water line, L, on a sailboat. A boat with an L of 16.5 feet can go 5.4 knots.
What is the variation constant?
:
That's the equation you have, just solve for k:
{{{sqrt(16.5)}}}*k = 5.4
:
Square both sides
16.5*k^2 = 5.4^2
:
16.5*k^2 = 29.16
k^2 = {{{29.16/16.5}}}
k^2 = 1.7673
k = {{{sqrt(1.7673)}}}
k = 1.33 is the variation constant
:
:
The formula for this design: S = 1.33{{{sqrt(L)}}}
;
Check our solution. let L = 16.5
S = 1.33{{{sqrt(16.5)}}}
S = 1.33 * 4.06
S = 5.3998 ~ 5.4