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?

Solution: 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

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?

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:

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