Final answer:
The person's velocity on the yacht is the resultant of the yacht's velocity and the river current's velocity, which is a vector sum that considers both magnitude and direction.
Step-by-step explanation:
If a person is sitting in a yacht that is going 25 knots per hour on a river with a current of 7 knots per hour, the person's velocity is whatever the yacht and current's resultant velocity is. This is because the velocity of the person on the yacht would be the vector sum of the yacht's velocity and the current's velocity. The velocity of an object in a fluid (like water) is always relative to something. In the case of a yacht in a river, the final velocity would be determined by adding the velocity of the yacht to the velocity of the river current, considering both magnitude and direction.
In the case of adding velocities: A boat attempts to travel straight across a river at a speed of 3.8 m/s, and the river current flows at a speed of 6.1 m/s to the right. We'd have to use a coordinate system to find the total velocity and direction of the boat relative to an observer on the shore, Vtot. The same principle applies to the person on the yacht - they would need to consider both the velocity of the boat and the current to find the resultant velocity relative to the shore.