# Why does a swimmer take longer to complete a trip in a river with a current?

• Ab17
In summary: So, what is the velocity of the swimmer?In summary, the conversation discussed a problem involving a swimmer in a river with a steady speed of 0.500 m/s. The student swims upstream a distance of 1.00 km and then swims back to the starting point. The questions asked were about the time it takes for the trip and why it takes longer when there is a current. The equations used were Vse = Vsr - Vre and the swimmer's velocity was found using vector addition. It was determined that the swimmer's velocity should be added for upstream and subtracted for downstream.
Ab17

## Homework Statement

A river has a steady speed of 0.500 m/s. A student swims M upstream a distance of 1.00 km and swims back to the Q/C starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim
take longer when there is a current?

Vse = Vsr - Vre

## The Attempt at a Solution

I done this problem by adding the velocity of the swimmer and current vectorialy to get the relative speed if student w.r.t to Earth then when I searced for the solution they had just added the two speed for the upward motion and subtracted them for downward motion. I am really confused i don't know what's going on

Break the question up in two parts. First, find the relative velocity of the swimmer with the shore going upstream and use this to find the time. Do the same again for downstream.

Must I do it vectorially?

I would. It makes it easier to understand, in my opinion.

I got 1.09 m/s relative to the earth

How did you get that?

Sqrt((1.2)^2 - (0.5)^2)

The velocity of the river and the velocity of the swimmer are not perpendicular to one another. Upstream means that the swimmer is parallel to the river but is working against the current. Downstream means that the current is pushing the swimmer. Knowing this, what would the addition of the vectors be in both the upstream case and the downstream one?

This is what I done

#### Attachments

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There will be no components for the vectors that's explains why they were just adding for going upstream and subtracting for downstream

Right. You have the swimmer on an angle but the question just says upstream, not going to the other bank or something like that.

## 1. What is the impact of river currents on a swimmer?

The impact of river currents on a swimmer depends on the strength and direction of the current. Strong currents can make it difficult for a swimmer to move forward, while weaker currents may provide little resistance. Swimmers can use the current to their advantage by swimming with the flow to conserve energy.

## 2. How does the shape of a river affect a swimmer's movement?

The shape of a river can have a significant impact on a swimmer's movement. Wide and shallow rivers may have a slower current, making it easier for a swimmer to move, while narrow and deep rivers may have a stronger current, making it more challenging for a swimmer to navigate. Additionally, bends and turns in a river can create eddies and back currents, which can affect a swimmer's path.

## 3. What techniques can a swimmer use to move efficiently in a river?

A swimmer can use several techniques to move efficiently in a river. One technique is to use the current to their advantage by swimming with the flow. Another technique is to use a side-stroke or breaststroke, which can help a swimmer maintain their position in the water while also providing some resistance against the current. Additionally, using a swimmer's body position and arm movements can also help them navigate through a river more efficiently.

## 4. How does a swimmer's body position affect their movement in a river?

A swimmer's body position plays a crucial role in their movement in a river. A streamlined body position with the head looking forward can help reduce drag and make it easier to move through the water. Additionally, keeping the body in a horizontal position can also help a swimmer move more efficiently, as it allows for better use of arm and leg movements.

## 5. What safety precautions should a swimmer take when swimming in a river?

When swimming in a river, it is essential to take safety precautions to ensure a safe and enjoyable experience. Swimmers should be aware of their surroundings and potential hazards, such as strong currents, submerged objects, and changing water depths. It is also recommended to swim with a buddy and wear a life jacket to help stay afloat in case of an emergency. Additionally, swimmers should avoid swimming in rivers after heavy rain or during flood conditions, as the water can be unpredictable and dangerous.

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