# How Far From Shore Is the Dog After Walking on the Boat?

• JWDavid
In summary, the dog weighing 10.8 lb stands 21.4 ft from shore on a flatboat. He walks 8.5 ft towards the shore and halts, while the boat weighs 46.4 lb and has no friction with the water. The center of mass of the boat + dog does not move, meaning the boat moves 1.6 feet in the water, the dog moves 8.5 feet on the boat, and the final distance from shore is 14.5 feet. The proportion of the dog's movement is calculated based on his weight and the total weight of 57.2 lb.
JWDavid

## Homework Statement

A dog weighing 10.8 lb, is standing on a flatboat so that he is 21.4 ft from shore. He walks 8.5 ft on the boat toward shore and then halts. The boat weighs 46.4 lb, and one can assume there is no friction between it and the water. How far is he from shore at the end of this time? (Hint: The center of mass of the boat + dog does not move. Why?)

## The Attempt at a Solution

Initially I considered that the boat will move exactly as much as the dog does, but I'm no longer sure it will. I am now of the opinion that maybe the dog will move a proportional distance of

8.50 ft x (his weight/total weight)

But I am not sure and would like a second opinion.

Hi JWDavid!
JWDavid said:
A dog weighing 10.8 lb, is standing on a flatboat so that he is 21.4 ft from shore. He walks 8.5 ft on the boat toward shore and then halts. The boat weighs 46.4 lb, and one can assume there is no friction between it and the water. How far is he from shore at the end of this time? (Hint: The center of mass of the boat + dog does not move. Why?)

Initially I considered that the boat will move exactly as much as the dog does, but I'm no longer sure it will. I am now of the opinion that maybe the dog will move a proportional distance of

8.50 ft x (his weight/total weight)

Nooo … if that were right, then the lighter the dog was, the less he would move …

but if he were a flea, the boat would stay still, and the proportion would be 1 (roughly) .

Hint: in problems like this, it's usually best to give letters to things … call the dog D, and the centre of the boat B, and the old and new centres of mass P and Q, and then calculate where P and Q are.

So I think I've gotten it: Here's what I did please confirm.

cm1 = (10.8*0 + 46.4*(L/2))/57.2 = .4L
cm2 = (10.8*8.5 + 46.4*(L/2))/57.2 = .4L + 1.6

cm2 - cm1 = 1.6 which ..? means the boat moves under the dog 1.6 feet

so the final answer is 21.4 - 8.5 + 1.6 = 14.5 feet - is this correct?

JWDavid said:
cm2 - cm1 = 1.6 which ..? means the boat moves under the dog 1.6 feet

so the final answer is 21.4 - 8.5 + 1.6 = 14.5 feet - is this correct?

Yup!

(except, technically i'd say that the boat moves 1.6 feet in the water, but 8.5 feet under the dog, and the dog moves 8.5 feet on the boat )

(and don't forget you're expected to answer "The center of mass of the boat + dog does not move. Why?", which you haven't yet shown)

## 1. What is CTR Mass?

CTR Mass stands for center of total resistance mass. It is a term used in naval architecture to describe the point on a boat where all the forces acting on the boat are balanced.

## 2. What does "dog walking on boat" mean?

"Dog walking on boat" is a colloquial term used to describe a phenomenon where a boat or ship heels or rolls excessively, causing it to appear as if it is being walked by a dog. This can happen due to various factors such as strong winds, rough seas, or an improper center of mass distribution on the boat.

## 3. How does dog walking on boat affect the CTR Mass?

Dog walking on boat can cause the CTR Mass to shift, leading to an imbalance in the forces acting on the boat. This can make the boat unstable and difficult to control, potentially leading to capsizing or other dangerous situations.

## 4. How can CTR Mass be calculated for a dog walking on boat scenario?

To calculate the CTR Mass for a dog walking on boat scenario, various factors such as the boat's dimensions, weight distribution, and the angle of heel must be taken into consideration. It is a complex calculation that is usually done by naval architects using specialized software.

## 5. How can dog walking on boat be prevented?

To prevent dog walking on boat, it is important to properly distribute weight on the boat and ensure that the CTR Mass is in the correct position. This can be achieved through careful design and construction of the boat, as well as proper loading and distribution of cargo. Additionally, experienced captains can also use techniques such as adjusting the sails and ballast to maintain stability and prevent excessive heel or roll.

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