# Relative Motion: Ferry Problem

• planke
In summary, the passenger's velocity is north relative to the ferry, and the ferry's velocity is west relative to the water.
planke

## Homework Statement

A passenger walks from one side of a ferry to the other as it approaches a dock. If the passenger's velocity is 1.90 m/s due north relative to the ferry, and 4.5 m/s at an angle of 33.0° west of north relative to the water, what are the direction and magnitude of the ferry's velocity relative to the water?

_____ degrees west of north
_____ m/s

## Homework Equations

Vfw = Vfp + Vwp
theta (angle) = tan-1 (Ay/Ax)
A (magnitude) = sqroot (Ax^2 + Ay^2)

## The Attempt at a Solution

Vfw = 1.9 ^y + (-4.5) cos (33) ^x

theta = tan-1 (1.9 / -4.5 cost (33)) = -26.7 degrees
magnitude = sqroot (1.9^2 + (-4.5 cos (33))^2) = 4.2 m/s

I don't understand what I did wrong.

I think you just found a few equations and are jamming in the numbers you found in the question in hope of getting the right answer. I'm not sure where you made your mistake because the proper way to do the question into understand what is really happening. I'm not sure what level of physics you are doing right now but this is how I would solve the problem:

Break up into x and y components (I would suggest x being the east and west direction and y being the north and south direction).

y components: (note that whether to use cos and sin for this part can most easily be found by drawing out the vectors)

Vpw = Vfw + Vpf
4.5 cos33 = Vfw + 1.9
=> Vfw = -1.87

x components:

Vpw = Vfw + Vpf
4.5sin33 = Vfw + 0
=> Vfw = 2.45

The magnetude and direction of the vector can be found using the formulas that you posted

planke said:
Vfw = Vfp + Vwp
That should be:

Vfw + Vwp = Vfp

Vfw = 1.9 ^y + (-4.5) cos (33) ^x
Don't forget that Vwp has both x and y components. Note that the angle is given with respect to north (the y-axis, not the x-axis), so you'll need to redo the x-component.

Last edited:

## 1. What is relative motion?

Relative motion is the concept of describing the motion of an object in relation to another object or frame of reference. It takes into account the perspective and movement of both objects.

## 2. What is the "Ferry Problem" in relative motion?

The "Ferry Problem" is a classic physics problem that involves a ferry crossing a river with a constant velocity while a swimmer swims across the river with a different velocity. It demonstrates how relative motion can affect the perceived motion of different objects.

## 3. How do you calculate the relative velocity in the "Ferry Problem"?

The relative velocity in the "Ferry Problem" can be calculated by subtracting the velocity of one object from the velocity of the other object. In this case, it would be the velocity of the swimmer relative to the ferry or the velocity of the ferry relative to the swimmer.

## 4. How does the angle of the river affect the "Ferry Problem"?

The angle of the river does not affect the "Ferry Problem" as the problem assumes that the river is straight and the velocity of the ferry and swimmer are constant. However, in real-world situations, the angle of the river can play a role in determining the relative velocity and the crossing time.

## 5. What are some real-world applications of relative motion?

Relative motion is used in various fields, including physics, engineering, and navigation. Some real-world applications include predicting the motion of objects in space, calculating the trajectory of moving vehicles, and determining the position of ships and aircraft in relation to each other.

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