Whenever we have a problem about a boat or swimmer crossing a river, it's safe to assume it's a two-dimensional relative motion problem. The steps to solve a problem like this are going to be:
- Organize information: the variables involved in a problem like this are velocities, distances, and time. It's always a good idea to draw yourself a diagram and label knowns to help you visualize the information!
- Combine velocities.
- Solve for the target variable.
In general, the equation we'll use to add velocities is:
In this problem, the swimmer has some velocity compared to the water of the river, and the river also moves with a velocity relative to the ground. If someone on the riverbank measured the swimmer's velocity, it would be the sum of those two vectors—we'll call that the "effective velocity" or veff.
We may also need the equation relating constant velocity to displacement: