Boat builders share an old rule of thumb for sailboats. The maximum speed 𝐾 in

Question

Boat builders share an old rule of thumb for sailboats. The maximum speed 𝐾 in

knots is 1.35 times the square root of the length 𝐿 in feet of the boat’s 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?

Answer 1

Robin/Jill/Bill/Vince -- please use the same name for your posts.

Answer 2

Jim -- not Jill

Answer 3

I am only Bill and Vince not the other ones

Answer 4

Thanks for not answer my question though :) really appreciate it

Answer 5

To determine the length of the waterline needed for a sailboat with a maximum speed of 8 knots, we can use the formula provided: 𝐾 = 1.35√𝐿.

1. Let's substitute the given maximum speed of 8 knots into the formula:
8 = 1.35√𝐿

2. Now, we can solve for 𝐿 by isolating the square root term:
√𝐿 = 8 / 1.35

3. Simplifying the right side of the equation:
√𝐿 ≈ 5.9259

4. Squaring both sides to isolate 𝐿:
𝐿 ≈ (5.9259)^2
𝐿 ≈ 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: 𝐾 = 1.35√𝐿.

2. Substitute the new maximum speed of 10 knots into the formula:
10 = 1.35√𝐿

3. Isolate the square root term on one side:
√𝐿 = 10 / 1.35

4. Simplify the right side:
√𝐿 ≈ 7.4074

5. Square both sides of the equation:
𝐿 ≈ (7.4074)^2
𝐿 ≈ 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.