# Swimmer's velocity relative to the shore (vectors)

• ulfy01
In summary, the swimmer is training in a river with a current of 1.33 metres per second. Their speed relative to the water is 2.86 metres per second. When swimming upstream, the swimmer's speed relative to the shore is 1.53 metres per second. This is because the swimmer is not swimming across the river, but rather against the current. This can be visualized by imagining a runner on a train heading in the opposite direction of the runner's movement.
ulfy01

## Homework Statement

A swimmer is training in a river. The current flows at 1.33 metres per second and the swimmer's speed is 2.86 metres per second relative to the water. What is the swimmer's speed relative to the shore when swimming upstream? What about downstream?

Pythagoras.

## The Attempt at a Solution

Here's my problem. Because we're looking at vectors, I would normally do the vector sum of both the velocities and use Pythagoras, as both given vectors are perpendicular.

Vcurrent = 1.33 m/s
Vswimmer relative to water = 2.86 m/s

So the resultant vector would be: $\sqrt{}$(1.332 + 2.862)

Giving 3.15 m/s, however this is wrong, as the answer given is 1.53 m/s upstream.

I'm puzzled as to how this answer was reached.

The swimmer is not swimming across the river.
He is swimming against the current. That how normally swimmers trainned.
Now imagine you running in direction to the east at a speed 1.33 metres per second on a train with 1.33 metres per second speed heading west.
To the man on the platform seeing you not moving, but with respect of the train you are running at 1.33 metres per second in easterly direction.

Hi, ulfy01.

Note that "swimming upstream" means swimming in a direction opposite to the current, not perpendicular to the current. So, there is no right triangle here.

[oops: I'm a bit late here, sorry.]

I just realized this and made a fool of myself, really. Way to overthink a problem and not read it properly. I'll go hide in a corner now. Thanks azizlwl!

I would approach this problem by first defining the direction of the current and the swimmer's velocity relative to the shore. Let's say the current is flowing downstream and the swimmer is swimming upstream. In this case, the swimmer's velocity relative to the shore would be the difference between their velocity relative to the water (2.86 m/s) and the velocity of the current (1.33 m/s).

This can be visualized as the swimmer trying to swim against the current, so their actual speed relative to the shore would be slower than their speed relative to the water. Using the Pythagorean theorem to find the resultant velocity would not be correct in this situation.

To find the swimmer's speed relative to the shore when swimming upstream, we can use the following equation:

Vs = Vw - Vc

Where:
Vs = swimmer's velocity relative to the shore
Vw = swimmer's velocity relative to the water
Vc = velocity of the current

Plugging in the given values, we get:

Vs = 2.86 m/s - 1.33 m/s = 1.53 m/s

This is the correct answer given in the problem.

For swimming downstream, the swimmer's velocity relative to the shore would be the sum of their velocity relative to the water and the velocity of the current:

Vs = Vw + Vc = 2.86 m/s + 1.33 m/s = 4.19 m/s

So the swimmer's speed relative to the shore when swimming downstream would be 4.19 m/s. This approach takes into account the direction of the current and the swimmer's velocity relative to the shore, and gives us the correct answer for both upstream and downstream swimming.

## 1. How is a swimmer's velocity relative to the shore calculated?

The swimmer's velocity relative to the shore is calculated by taking into account both the swimmer's speed and direction in relation to the shore. This is done using vector addition, where the swimmer's velocity vector is added to the velocity vector of the current or any other external forces acting on the swimmer.

## 2. Why is it important to consider the swimmer's velocity relative to the shore?

Considering the swimmer's velocity relative to the shore is important because it helps determine the overall speed and efficiency of the swimmer. By taking into account the direction and magnitude of the swimmer's velocity in relation to the shore, we can better understand the impact of external forces and make adjustments for a more efficient swim.

## 3. How does the swimmer's velocity relative to the shore affect their performance?

The swimmer's velocity relative to the shore directly affects their performance, as it determines the speed at which they are moving towards their destination. A swimmer with a higher velocity relative to the shore will have a faster overall speed and may be able to overcome external forces such as currents more easily.

## 4. Can a swimmer's velocity relative to the shore change during a swim?

Yes, a swimmer's velocity relative to the shore can change during a swim. This can occur due to changes in the direction or strength of the current, or by the swimmer adjusting their speed or direction. It is important for the swimmer to continuously monitor their velocity relative to the shore and make adjustments as needed for optimal performance.

## 5. How can a swimmer improve their velocity relative to the shore?

A swimmer can improve their velocity relative to the shore by increasing their overall swimming speed and efficiency. This can be achieved through techniques such as proper body positioning, efficient use of arms and legs, and reducing drag in the water. Additionally, understanding and utilizing the effects of external forces such as currents can also help improve a swimmer's velocity relative to the shore.

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