A river flows with a uniform velocity 𝐯 . A person in a...

A river flows with a uniform velocity $\mathbf{v} . A$ person in a motorboat travels $1.00 \mathrm{~km}$ upstream, at which time she passes a log floating by. Always with the same throttle setting, the boater continues to travel upstream for another $60.0 \mathrm{~min}$ and then returns downstream to her starting point, which she reaches just as the same log does. Find the velocity of the river.

Key Concepts

Algebraic Problem Solving

Many motion problems require setting up and solving systems of equations. By applying algebraic techniques to relate different segments of the journey, one can isolate and solve for the unknown parameters such as the speed of the river.

Time-Distance-Speed Relationship

The fundamental relationship between time, distance, and speed is that distance equals speed multiplied by time. This relationship is used to model various segments of the journey in riverboat problems and to set up equations for solving unknowns like the river’s velocity.

Relative Motion

This concept involves understanding how the motion of an object is influenced by the speed and direction of the medium in which it moves. In problems involving rivers, the boat’s velocity relative to the water needs to be combined with the river’s current to determine the effective velocity relative to the shore.

Frames of Reference

Choosing an appropriate frame of reference is essential when analyzing motion. In river problems, it is important to distinguish between the boat’s speed relative to the water and its speed relative to the ground, which involves adding or subtracting the velocity of the river.

Uniform Motion

Uniform motion refers to movement at a constant speed in a straight line, meaning that the distance traveled is directly proportional to the time taken. This principle underpins the setup of equations relating distance, time, and velocity in the problem.

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