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
42R？
and traveling at a speed of 6 m/s experiences a drag force of 504 N. Determine the drag force on a boat with a wet surface area of 56 m² traveling at a speed of 8 m/s.
Given:
A1 = 42 m²
s1 = 6 m/s
F1 = 504 N
We can write the equation for drag force as:
F = k * A * s²
Plugging in the values for the first boat:
504 = k * 42 * 6²
504 = 1512k
k = 504 / 1512
k = 1/3
Now, we can calculate the drag force for the second boat:
A2 = 56 m²
s2 = 8 m/s
F2 = (1/3) * 56 * 8²
F2 = (1/3) * 56 * 64
F2 = 2992 N
Therefore, the drag force on a boat with a wet surface area of 56 m² traveling at a speed of 8 m/s is 2992 N.