A boat is traveling across a river at 5.0 m/s relative to the water. The river is flowing at 3.0 m/s relative to the ground. If the boat's velocity is perpendicular to the river's current, what is the boat's speed relative to the ground?

Core Concept

Since the boat's velocity is perpendicular to the river's current, we can use the Pythagorean theorem to find the resultant velocity. The boat's velocity relative to the ground is the vector sum of its velocity relative to the water and the water's velocity relative to the ground. Thus, v_ground = √(5.0² + 3.0²) = √(25 + 9) = √34 ≈ 5.8 m/s. Option A is incorrect as it's the difference between the two velocities, which would be the case if they were in opposite directions. Option B is incorrect as it's the average of the two velocities. Option D is incorrect as it's the sum of the two velocities, which would be the case if they were in the same direction.