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. A boat with a wet surface area of 50ft'2 traveling at 7mph experiences a drag force of 98N. Find the wet surface area of a boat traveling 7.5mph and experiencing a drag force of 135N .
We know that F varies jointly with A and S^2, so we can write:
F = k * A * S^2
where k is the constant of proportionality.
To find k, we can use the information given in the first part of the problem:
98 = k * 50 * 7^2
Solving for k, we get:
k = 98 / (50 * 49) = 0.04
Now we can use this value of k to find the wet surface area of the boat in the second part of the problem:
135 = 0.04 * A * 7.5^2
Solving for A, we get:
A = 135 / (0.04 * 7.5^2) = 120 ft^2
Therefore, the wet surface area of the boat traveling at 7.5 mph and experiencing a drag force of 135N is 120 ft^2.