# What is the speed of the boat relative to the water?

• Lori
In summary, we need to consider the velocity vector that is relative to the water in order to determine the boat's speed relative to the water. This vector is angled upwards against the stream and is necessary in order to reach a shifting goal (our destination on the land). We should also keep in mind that the Earth is rotating but for the sake of simplicity, we will consider the land as fixed.
Lori

## Homework Statement

A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?

I'm mostly concerned about the wording and which part of the "triangle" that the answer is referring to!

2. Homework Equations

V = D/T

## The Attempt at a Solution

V = 0.14/20 = 7m

Hey!
Can someone help me explain how the speed of the boat relative to the water would be referring to the velocity in the y direction for the boat? How do i know that it isn't referring to the hypotenuse ? Overall, i usually get confused with the wording for "relative to _____" because I don't know which part of the triangle it would be a part of!

If i didn't know that the speed of the boat relative to the water is in the y direction, then i wouldn't know that i could just use the formula V = D/T!

For instance, I would think the boat's speed relative to the water is different from the boat's speed relative to the earth/ground

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Please show your vector diagram for the boat in this situation. Show the boat and the river vectors -- those will help you to gain intuition and solve the problem. Please show your work. thanks.

berkeman said:
Please show your vector diagram for the boat in this situation. Show the boat and the river vectors -- those will help you to gain intuition and solve the problem. Please show your work. thanks.

How would i know that the boat's speed relative to the water is referring to the hypotenuse or the vertical direction in my sketch?

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Lori said:
How would i know that the boat's speed relative to the water is referring to the hypotenuse or the vertical direction in my sketch?
Hey Lori! :)

You seem to have everything in place already.
The vertical direction is relative to the land, which is explicitly given.
To get there, we need a velocity vector that is at an angle to compensate for the flowing river (the hypotenuse).
That vector is relative to the water.

I like Serena said:
Hey Lori! :)

You seem to have everything in place already.
The vertical direction is relative to the land, which is explicitly given.
To get there, we need a velocity vector that is at an angle to compensate for the flowing river (the hypotenuse).
That vector is relative to the water.

Thanks! Will the vector that is relative to the water always be the vector that is affected by the current? So, the vector that the boat heads to in its own point of which is north would always be the velocity relative to the ground/earth?

I often mix the vectors up and end up getting the wrong triangle sketch or end up finding the answer for the wrong side of the triangle!

Lori said:
Thanks! Will the vector that is relative to the water always be the vector that is affected by the current? So, the vector that the boat heads to in its own point of which is north would always be the velocity relative to the ground/earth?

I often mix the vectors up and end up getting the wrong triangle sketch or end up finding the answer for the wrong side of the triangle!
That's a pretty common mixup. ;)

Anyway, the vector that is relative to the water is the one that we aim for when steering.
In our case it's angled upward against the stream.

Any point that is fixed on the earth, that is, our starting point and our destination point, are just that - they are relative to the earth.
Then again, the Earth is also rotating, but we pretend that it's not, and that the land is fixed. We are not considering how our Earth has moved in space for these problems.
Similarly, when we are actually in the water, the water is (sort of) fixed as well, and we move with respect to the water.
It's just that our destination point (north and fixed on the land) is shifting, so we need to go diagonal and upstream with respect to the water in order to reach that shifting goal. And if we don't hurry up, we'll 'miss' our goal.

Lori
I like Serena said:
That's a pretty common mixup. ;)

Anyway, the vector that is relative to the water is the one that we aim for when steering.
In our case it's angled upward against the stream.

Any point that is fixed on the earth, that is, our starting point and our destination point, are just that - they are relative to the earth.
Then again, the Earth is also rotating, but we pretend that it's not, and that the land is fixed. We are not considering how our Earth has moved in space for these problems.
Similarly, when we are actually in the water, the water is (sort of) fixed as well, and we move with respect to the water.
It's just that our destination point (north and fixed on the land) is shifting, so we need to go diagonal and upstream with respect to the water in order to reach that shifting goal. And if we don't hurry up, we'll 'miss' our goal.
Thanks so much, you really cleared up any doubts that i have with these kind of problems.

I like Serena

## 1. What is the speed of the boat relative to the water?

The speed of the boat relative to the water refers to the velocity of the boat in relation to the water's surface. This can also be referred to as the boat's speed over ground, as it takes into account the movement of the water as well.

## 2. How is the speed of the boat relative to the water calculated?

The speed of the boat relative to the water is calculated by subtracting the velocity of the water from the velocity of the boat. This can be determined using GPS or by measuring the boat's movement against stationary objects on the water's surface.

## 3. What factors can affect the speed of the boat relative to the water?

The speed of the boat relative to the water can be affected by various factors such as wind speed and direction, current, and the shape and design of the boat's hull. These factors can either increase or decrease the boat's speed relative to the water.

## 4. Is the speed of the boat relative to the water the same as its speed through the water?

No, the speed of the boat relative to the water and its speed through the water are not the same. The speed through the water only takes into account the boat's movement through the water, while the speed relative to the water also considers the movement of the water itself.

## 5. Why is it important to know the speed of the boat relative to the water?

Knowing the speed of the boat relative to the water is important for various reasons. It can help with navigation and determining the boat's position, as well as understanding the effects of external factors such as wind and current. It can also be used to calculate the boat's fuel consumption and estimate travel time.

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