Boat builders share an old rule of thumb for sailboats. The maximum speed ๐พ in
knots is 1.35 times the square root of the length ๐ฟ in feet of the boatโs waterline. If a customer is planning
on ordering a sailboat with a maximum speed of 8 knots how long should the waterline be? How much
longer would the waterline have to be to achieve a maximum speed of 10 knots?
Robin/Jill/Bill/Vince -- please use the same name for your posts.
Jim -- not Jill
I am only Bill and Vince not the other ones
Thanks for not answer my question though :) really appreciate it
To determine the length of the waterline needed for a sailboat with a maximum speed of 8 knots, we can use the formula provided: ๐พ = 1.35โ๐ฟ.
1. Let's substitute the given maximum speed of 8 knots into the formula:
8 = 1.35โ๐ฟ
2. Now, we can solve for ๐ฟ by isolating the square root term:
โ๐ฟ = 8 / 1.35
3. Simplifying the right side of the equation:
โ๐ฟ โ 5.9259
4. Squaring both sides to isolate ๐ฟ:
๐ฟ โ (5.9259)^2
๐ฟ โ 35.0571
So, the waterline length of the sailboat should be approximately 35.0571 feet to achieve a maximum speed of 8 knots.
Next, let's find out how much longer the waterline would have to be to achieve a maximum speed of 10 knots:
1. We'll use the same formula: ๐พ = 1.35โ๐ฟ.
2. Substitute the new maximum speed of 10 knots into the formula:
10 = 1.35โ๐ฟ
3. Isolate the square root term on one side:
โ๐ฟ = 10 / 1.35
4. Simplify the right side:
โ๐ฟ โ 7.4074
5. Square both sides of the equation:
๐ฟ โ (7.4074)^2
๐ฟ โ 54.7613
Therefore, the waterline would have to be approximately 54.7613 feet longer to achieve a maximum speed of 10 knots compared to the initial maximum speed of 8 knots.