# Find the velocity of the swimmer relative to the shore

• larryboi7
In summary, a swimmer is moving at a constant speed of 5mph at a direction of 30 degrees south of east relative to the water, while a current is flowing at a constant speed of 1.5mph at a direction of 30 degrees west of north. To find the velocity of the swimmer relative to the shore, we can use the equation vSL = vSW + vWL. After 2 hours, the swimmer's displacement can be found by multiplying the velocity by the time. If the swimmer were to swim unaware of the current, the distance from the target position can be calculated by using the Pythagorean theorem.
larryboi7

## Homework Statement

A swimmer is moving 30 degrees south of east at a constant speed of 5mph relative to the water. A current is flowing 30 degrees west of north at a constant speed of 1.5mph.

Find the velocity of the swimmer relative to the shore. After 2 hours, what is the swimmers displacement? How FAR is the swimmer from his target position if he swam unaware of the current?

Vsl = Vsw + Vwl
Vox = Vo(cos30)
Voy = Vo(sin30)

## The Attempt at a Solution

Vox = 5cos30 = 4.33
Voy = 5sin30 = 2.5

Last edited:
Surely you must have some idea?

CompuChip said:
Surely you must have some idea?

I wouldn't have asked if I knew...

Hehe, obviously I didn't expect you to say "yes, I know the answer already, I just want to check if you know it".
But when asking questions about homework, we would like you to show some work which you have already tried, even if you think it is leading you nowhere.

Does an equation like
vSW + vWL = vSL
sound familiar,
where vSW is the velocity vector of the swimmer relative to the water, vWL of the water relative to the land, and vSL of the swimmer relative to the land

CompuChip said:
Hehe, obviously I didn't expect you to say "yes, I know the answer already, I just want to check if you know it".
But when asking questions about homework, we would like you to show some work which you have already tried, even if you think it is leading you nowhere.

Does an equation like
vSW + vWL = vSL
sound familiar,
where vSW is the velocity vector of the swimmer relative to the water, vWL of the water relative to the land, and vSL of the swimmer relative to the land

Yes, it does look familiar. I just have hard time setting it up. The problem I have now it finding the velocities. I believe the equations I presented are correct?

## What is the definition of velocity?

Velocity is a vector quantity that represents the rate of change of an object's position with respect to time. It includes both the magnitude and direction of an object's motion.

## How is velocity different from speed?

Velocity and speed are often used interchangeably, but they have distinct meanings in physics. Velocity is a vector quantity that includes direction, while speed is a scalar quantity that only represents magnitude.

## What is the formula for calculating velocity?

The formula for velocity is v = d/t, where v is velocity, d is distance traveled, and t is time taken. Velocity can also be calculated by taking the derivative of an object's position function with respect to time.

## How is the velocity of a swimmer relative to the shore determined?

The velocity of a swimmer relative to the shore can be determined by measuring the swimmer's speed and direction of motion with respect to the shore. This can be done using a GPS device or by measuring the swimmer's position at different points in time.

## What factors can affect the velocity of a swimmer relative to the shore?

The velocity of a swimmer relative to the shore can be affected by factors such as the swimmer's physical abilities, water currents, wind speed, and direction. The swimmer's technique and the type of stroke used can also impact their velocity.

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