# What's their velocity relative to the water?

• Sean1218
In summary, relative velocity is the velocity of an object in reference to another object, taking into account their motion and direction. It is calculated by subtracting the velocity of the reference object from the velocity of the moving object. Knowing the relative velocity is important in analyzing the motion of objects and is used in fields like physics, engineering, and navigation. Relative velocity differs from absolute velocity in that it is in relation to another moving object, and it can be negative if the objects are moving in opposite directions.
Sean1218

## Homework Statement

Boat moving at 2.8 m/s [fwd] relative to water (VBW)
Tourists walking on deck at 1.1 m/s relative to deck (VPB)

Determine their velocity relative to the water if they are walking towards the starboard (right side of ship).

VPW = VPB + VBW

## The Attempt at a Solution

VPW = 1.1 m/s [R] + 2.8 m/s [fwd]

VPB = 1.1 m/s: x-dir = 0 and y-dir = 1.1 m/s
VBW = 2.8 m/s: x-dir = 2.8 m/s and y-dir = 0

VPW = ??: x-dir 2.8 m/s y-dir = 1.1 m/s

So do I just draw a graph? Like, 2.8 in magnitude along the positive x-axis, and then 1.1 in magnitude up (or how would I think about this? like how would I know where to draw the vectors and which direction etc. in a more complicated question?)

and just

c = sqrt(a2 + b2)
c = 3.01 m/s
VPW = 3.01 m/s

Then how do I find the direction of VPW?

[tan-1(1.1/2.8)] = [E 21.45 N] or [21.45 N of the horizontal] or what? since the question doesn't use direction

Also, how many significant digits should I leave my answers to (both velocity and direction)?

Last edited:

To find the direction of VPW, you can use the inverse tangent function as you did, but it is important to specify the direction in your answer. In this case, the direction would be approximately east of north (E 21.45 N). As for the number of significant digits, it is best to use the same number of significant digits as the given data. In this case, both VBW and VPB have 3 significant digits, so your final answer should also have 3 significant digits (3.01 m/s).

## 1. What is relative velocity?

Relative velocity is the velocity of an object in reference to another object. It takes into account the motion of both objects and their direction of movement.

## 2. How is relative velocity calculated?

Relative velocity is calculated by subtracting the velocity of the reference object from the velocity of the moving object. This can be done using vector addition or using the relative velocity formula: v12 = v1 - v2, where v12 is the relative velocity, v1 is the velocity of the moving object, and v2 is the velocity of the reference object.

## 3. What is the importance of knowing the relative velocity?

Knowing the relative velocity is important in analyzing the motion of objects in relation to each other. It helps in understanding how objects move and interact with each other, and is essential in fields such as physics, engineering, and navigation.

## 4. How does relative velocity differ from absolute velocity?

Absolute velocity is the velocity of an object in relation to a fixed reference point, while relative velocity is the velocity of an object in relation to another moving object. Absolute velocity does not change unless the reference point changes, while relative velocity can change depending on the motion of both objects.

## 5. Can relative velocity be negative?

Yes, relative velocity can be negative. This indicates that the moving object is moving in the opposite direction of the reference object. It is important to consider the sign of the relative velocity when analyzing the motion of objects.

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