How Far Is the Dog from the Shore After Walking on the Boat?

• anotherghost
In summary: Now find position of the dog.In summary, the problem involves a dog on a boat moving a distance L towards the shore from its initial position X. The equation used is based on the principle of center of mass, where the combined center of mass of the dog and boat remains the same before and after the dog's movement. The solution involves finding the new position of the boat's center of mass and using it to determine the position of the dog.
anotherghost

Homework Statement

All right, so: dog on a boat. It's the snoopy problem. There's a boat floating on some water, and there's a dog on the end - he starts at X away from the shore. Then, he walks a length L across the boat towards the shore. How far is he away from the shore at the end?

Homework Equations

m1r1 + m2r2 = (m1 + m2)rcm

The Attempt at a Solution

As far as I can get is to set the center of mass as X at the beginning.

Mboat * Xi + Mdog * Xi = (Mboat + Mdog)Xi

and then the dog walks L towards the shore and I am not sure how to set this equation up.

Mboat * (Xi + L) + Mdog * (Xi - L) = (Mboat + Mdog) Xi

See, I know the center of mass doesn't move, because the system is isolated and the only forces are internal. However, I don't know how to make the positions relative - this equation would work if the problem literally stated he walks a length L towards the shore (his new position obviously would be Xi - L) but it says he walks length L down the boat, which means the boat moves too and he doesn't quite make the distance L from an external observer's point of view.

In the given problem, the center of mass of boat and dog are not at Xi. Only CM of dog is at Xi. Let d be the CM of boat.
Now CM of (boat + dog) will be -------(1)
As you have said CM of the system remains the same. So when dog walks a length L towards the shore, CM of boat must move away from the shore. Let this be x. Now new position of the dog is [(X - L) + x] and new CM of boat wiil be (d + x). Find the CM of ( dog + boat) in this position and equate it to eq(1) and find x.

I understand your frustration with this problem. It can be challenging to visualize and set up equations for problems like these. However, it is important to remember that in physics, we often make simplifying assumptions in order to solve problems. In this case, we can assume that the boat is stationary and only the dog is moving. This means that the center of mass will remain at Xi at all times.

Using this assumption, we can set up the following equation:

Mdog * (Xi + L) = (Mdog) Xi

Solving for Xi, we get:

Xi = L/2

Therefore, at the end of the dog's walk, he will be L/2 away from the shore.

It's important to keep in mind that while this solution may not perfectly reflect the real world scenario, it allows us to solve the problem and gain a better understanding of the concepts involved. As scientists, we must be willing to make simplifying assumptions in order to make progress in our understanding of the natural world.

What is the meaning behind "Snoopy is killing me here"?

"Snoopy is killing me here" is a phrase used to express feelings of frustration, exhaustion, or being overwhelmed. It is often used in a humorous or exaggerated way to describe a difficult situation.

Is there a specific source or origin for this phrase?

The phrase "Snoopy is killing me here" is a popular catchphrase from the comic strip Peanuts, created by Charles M. Schulz. In the strip, the character Lucy often uses this phrase to express her frustration with her brother, Linus, and his beloved blanket.

Why is "Snoopy" mentioned specifically in this phrase?

"Snoopy" refers to the popular character from the comic strip Peanuts. He is a white beagle with black ears and a black nose, and is known for his playful and mischievous personality. In this phrase, "Snoopy" is used as a stand-in for any frustrating or overwhelming situation.

Is there a deeper meaning behind this phrase?

While the phrase is typically used in a lighthearted or humorous context, it can also be seen as a commentary on the struggles of everyday life. The character of Snoopy, who is portrayed as carefree and playful, can be seen as a symbol for the challenges and obstacles that we all face in life.

How is this phrase relevant in today's society?

In today's society, the phrase "Snoopy is killing me here" is commonly used in casual conversation and on social media to express feelings of frustration or exhaustion. It has become a popular and relatable phrase that is used to describe a variety of situations, from work or school stress to personal struggles.

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