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:

$\overline{){\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{\mathit{P}\mathit{A}}{\mathbf{=}}{\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{\mathit{P}\mathit{B}}{\mathbf{+}}{\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{\mathit{B}\mathit{A}}}$

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 *v _{eff}*.

$\overline{){\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{\mathit{e}\mathit{f}\mathit{f}}{\mathbf{=}}{\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{{\mathit{s}}}{\mathbf{+}}{\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}}_{{\mathit{r}}}}$

We may also need the equation relating constant velocity to displacement:

$\overline{)\stackrel{\mathbf{\rightharpoonup}}{\mathit{v}}{\mathbf{=}}\frac{\mathbf{\u2206}\stackrel{\mathbf{\rightharpoonup}}{\mathit{r}}}{\mathbf{\u2206}\mathit{t}}}$

A swimmer is capable of swimming 0.80 m/s in still water.**(a)** At what upstream angle must the swimmer aim, if she is to arrive at a point directly across a 55-m wide river whose current is 0.50 m/s?**(b)** How long will it take her?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Relative Velocity in 2D concept. You can view video lessons to learn Relative Velocity in 2D. Or if you need more Relative Velocity in 2D practice, you can also practice Relative Velocity in 2D practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Atta-Fynn's class at UTA.