Final answer:
The magnitude of the resultant force on the balloon is approximately 15.8 N.
Step-by-step explanation:
The magnitude of the resultant force on the balloon can be found using the Pythagorean theorem. In this case, the net force on the balloon is 4.0 N, which is the difference between the force of the wind (Fw) and the force of the current (Fc). Since we know the magnitudes of Fw and Fc, we can use the Pythagorean theorem to find the magnitude of the resultant force:
R = sqrt(Fw^2 + Fc^2)
Substituting the given values, we have:
R = sqrt(13.0^2 + 9.0^2)
R = sqrt(169 + 81)
R = sqrt(250)
R ≈ 15.8 N
Therefore, the magnitude of the resultant force on the balloon is approximately 15.8 N.