# Optimal Direction for Long-Distance Swimmer in Ocean Currents

• Mdhiggenz
In summary, a long-distance swimmer plans to swim from Port Angeles, WA to Victoria, B.C., a distance of 50km. The swimmer's speed in still water is 4km/h, but there is a 3km/h ocean current flowing from west to east. To make the crossing along a straight line between the two cities, the swimmer will need to swim at a direction of 49 degrees to counteract the current's effect. This can be solved using a velocity vector diagram or by calculating the components of the swimmer's velocity.
Mdhiggenz

## Homework Statement

A long-distance swimmer is able to swim through still water at 4 km/h. She wishes to try to swim from Port Angeles, WA, due north to Victoria, B.C., a distance of 50 km. An ocean current flows through the Strait of Juan de Fuca from west to east at 3 km/h. In what direction should she swim to make the crossing along a straight line between the two cities?

## The Attempt at a Solution

So I know I have to split it into its x and y components , however I have no idea how to start this problem.

The answer is 49 degrees

You need a velocity vector diagram showing the swimmer vector plus the current vector equaling a combined velocity vector straight north. You can solve the triangle with law of sines, law of cosines to find the swimmer velocity. Or solve it with x,y components and some algebra.

## 1. What is meant by "relative velocity of swimmer"?

The relative velocity of a swimmer is the speed at which they are moving in relation to another object or observer. It takes into account both the swimmer's speed and direction of movement, as well as the speed and direction of the other object or observer.

## 2. How is the relative velocity of a swimmer calculated?

The relative velocity of a swimmer can be calculated by subtracting the speed and direction of the other object or observer from the swimmer's speed and direction. This can be done using vector addition or by using the formula v = v1 - v2, where v is the relative velocity, v1 is the swimmer's velocity, and v2 is the velocity of the other object or observer.

## 3. Why is the concept of relative velocity important in swimming?

The concept of relative velocity is important in swimming because it helps swimmers understand their speed and motion in relation to other objects or observers. It can also help swimmers make strategic decisions in races, such as how to position themselves relative to their competitors.

## 4. Does the relative velocity of a swimmer change in different environments?

Yes, the relative velocity of a swimmer can change in different environments. Factors such as water current, wind, and turbulence can affect the relative velocity of a swimmer. Additionally, the relative velocity of a swimmer may also change depending on the speed and direction of the other objects or observers present in the environment.

## 5. How can understanding relative velocity improve a swimmer's performance?

Understanding relative velocity can improve a swimmer's performance by allowing them to make strategic decisions based on their speed and position in relation to their competitors. It can also help swimmers adjust their technique to account for environmental factors that may affect their relative velocity.

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