A swimmer, capable of swimming at a speed of 1.3 m/s in still water (i.e., the swimmer can swim with a speed of 1.3 m/s relative to the water), starts to swim directly across a 2.2-km-wide river. However, the current is 0.91 m/s, and it carries the swimmer downstream.

(a) How long does it take the swimmer to cross the river?
(b) How far downstream will the swimmer be upon reaching the other side of the river?

To find the answers to these questions, we need to consider the swimmer's velocity relative to the ground, taking into account both their swimming speed and the current of the river.

(a) To determine the time it takes the swimmer to cross the river, we can use the formula:

Time = Distance / Velocity

The swimmer needs to cross a river that is 2.2 km wide. However, the current is carrying the swimmer downstream, so the effective velocity is the sum of the swimmer's swimming speed and the current speed:

Effective Velocity = Swimming Speed + Current Speed

In this case, the swimming speed is 1.3 m/s, and the current speed is 0.91 m/s. So the effective velocity is:

Effective Velocity = 1.3 m/s + 0.91 m/s = 2.21 m/s

Now we can calculate the time it takes the swimmer to cross the river:

Time = Distance / Effective Velocity

Converting the distance from kilometers to meters:

Distance = 2.2 km * 1000 m/km = 2200 m

Time = 2200 m / 2.21 m/s ≈ 994.57 seconds

So, it takes the swimmer approximately 994.57 seconds, or about 16.57 minutes to cross the river.

(b) To determine how far downstream the swimmer will be upon reaching the other side of the river, we need to calculate the distance the current carries the swimmer during the crossing time.

Distance Downstream = Current Speed * Time

Using the current speed of 0.91 m/s:

Distance Downstream = 0.91 m/s * 994.57 s ≈ 904.45 meters

So the swimmer will be approximately 904.45 meters downstream when they reach the other side of the river.