A swimmer is heading straight for the other shore of a river with a velocity of vs=0.5 m/s relative to the water, but is carried away by the current, which has a velocity of vr=0.4 m/s. It takes her 20.6 s to get across. How far downstream does she end up?

To find the distance downstream that the swimmer ends up, we need to calculate the displacement caused by the current during the time it takes for the swimmer to reach the other shore.

Let's break down the problem step by step:

1. The swimmer's velocity with respect to the shore (Vs) is the vector sum of her velocity with respect to the water (vs) and the velocity of the current (vr). So we have:

Vs = vs + vr

Substituting the given values:

Vs = 0.5 m/s + 0.4 m/s
Vs = 0.9 m/s

2. Now, we need to find the time it takes for the swimmer to cross the river. From the question, we are given that it takes her 20.6 seconds.

3. The displacement caused by the current (d) can be calculated using the equation:

d = Vs * t

Substituting the given values:

d = 0.9 m/s * 20.6 s
d = 18.54 m

Therefore, the swimmer ends up 18.54 meters downstream.