A swimmer, capable of swimming at a speed of 0.8 m/s in still water (i.e., the swimmer can swim with a speed of 0.8 m/s relative to the water), starts to swim directly across a 2.5 km wide river. However, the current is 0.91 m/s, and it carries the swimmer downstream.
and the question?
(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 out how long it takes for the swimmer to cross the river, we need to consider the effect of the current on the swimmer's motion.
Let's break down the problem:
Given:
- Speed of the swimmer in still water: 0.8 m/s
- Width of the river: 2.5 km
- Speed of the current: 0.91 m/s
To calculate the time it takes to cross the river, we can use the following formula:
Time = Distance / Speed
First, we need to find the effective speed of the swimmer considering the current. Since the current is moving downstream, it will affect the swimmer's motion.
The effective speed of the swimmer can be calculated by subtracting the speed of the current from the swimmer's speed in still water:
Effective speed = Speed in still water - Speed of the current
Effective speed = 0.8 m/s - 0.91 m/s
Effective speed = -0.11 m/s
Notice that the effective speed is negative, indicating that the swimmer is moving against the current.
Now, we can calculate the time it takes for the swimmer to cross the river:
Time = Distance / Speed
Distance = 2.5 km = 2500 m
Speed = Effective speed = -0.11 m/s
Time = 2500 m / (-0.11 m/s)
Time ≈ -22727 seconds
The negative duration suggests that the effective speed is not enough to overcome the current, and the swimmer will not be able to cross the river directly. Please note that the negative sign merely indicates that the swimmer is moving against the current; it doesn't imply a negative physical time.