Answer: S = 237.2 mph
Explanation:
Given that the drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat.
That is. F = KAS^2
Where
F = drag force
K = proportionality constant
S = speed
A boat with a wet surface area of 50 ft^2 traveling at 7 mph experiences a drag force of 98N
1 square foot = 3.587×10^-8 square mile
A = 50 × 3.587×10^-8
A = 1.7935×10^-6
Using the derived formula
F = KAS^2
98 = K × 1.7935×10^-6 × 7^2
98 = 8.788x10^-5K
K = 1115.14
To Find the speed of a boat experiencing a drag force of 135 N and having a wet surface area of 60ft^2 . We will use the same formula
A = 60 × 3.587×10^-8
A = 2.1522×10^-6
F = KAS^2
135 = 1115.14 × 2.1522×10^-6 × S^2
S^2 = 56249.9
S = 237.2 mph