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 42 ft^2 traveling at 10 mph experiences a drag force of 210 N. Find the drag force of a boat having a wet surface area of 36 ft^2 ? and traveling 15 mph.
We know that the drag force F varies jointly with the wet surface area A and the square of the speed s. This can be represented as:
F = k * A * s^2
where k is a constant of variation.
Given that a boat with a wet surface area of 42 ft^2 traveling at 10 mph experiences a drag force of 210 N, we can plug these values into the equation to find k:
210 = k * 42 * 10^2
210 = k * 4200
k = 210 / 4200
k = 0.05
Now that we have the value of k, we can use it to find the drag force of a boat with a wet surface area of 36 ft^2 and traveling at 15 mph:
F = 0.05 * 36 * 15^2
F = 0.05 * 36 * 225
F = 81 * 225
F = 18225
Therefore, the drag force of the boat with a wet surface area of 36 ft^2 and traveling at 15 mph is 18225 N.