Final answer:
The resultant velocity of Kym's boat is 10.0 m/s at an angle of approximately 53.13° relative to the shore.
Step-by-step explanation:
The resultant velocity of Kym's boat can be found by adding the velocity of the boat with respect to the water (Vboat) and the velocity of the river (Vriver). Since the boat is moving straight across the river, the velocity of the boat with respect to the water is perpendicular to the velocity of the river. Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity (Vtot) as:
Vtot = √(Vboat^2 + Vriver^2)
Substituting the given values, Vboat = 8.0 m/s and Vriver = 6.0 m/s, we get:
Vtot = √(8.0^2 + 6.0^2) = √(64 + 36) = √100 = 10.0 m/s
The direction of the resultant velocity relative to the shore can be determined using the tangent function:
θ = tan^(-1)(Vboat/Vriver)
Substituting the given values, we get:
θ = tan^(-1)(8.0/6.0) = tan^(-1)(4/3)
Using a calculator, θ ≈ 53.13°
Therefore, Kym's resultant velocity relative to the shore is 10.0 m/s at an angle of approximately 53.13° (northwest direction).