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Boat-man problem, velocity of center of mass

  • Thread starter Dansuer
  • Start date
  • #1
81
1

Homework Statement



A man of mass 84.4 Kg is in the back of a boat of mass 425 kg which is moving without friction on ice with velocity 4.16 m/s. the man moves from the back to the top of the boat with velocity 2.08 m/s traveling for 18.2m. How much distance does the boat travel while the man moves?

Homework Equations



v[tex]_{cm}[/tex] = (v[tex]_{1}[/tex]m[tex]_{1}[/tex] + v[tex]_{2}[/tex]m[tex]_{2}[/tex])/(m[tex]_{1}[/tex]+m[tex]_{2}[/tex])

The Attempt at a Solution



The way i try to solve this was that i put V[tex]_{cm}[/tex] = 0 because i choose a coordinate system with velocity V[tex]_{cm}[/tex]. The equation on top gives the velocity of the boat to be 0.41 m/s. Subtract this to the velocity of the boat relative to the ice gives v=3.7 m/s
Now i calculated the distance travelled: 18.2 : 2.08 = x : 3.7 which is 32.37

but it's not the same results as the book gives as a solution. What did i do wrong?
 

Answers and Replies

  • #2
1,137
0
why are you taking the frame at velocity of CM. take frame at v=0
then you dont need to find the relative speeds, just use them as given
 
  • #3
81
1
You're right i could've done that. But the answer to the problem does not change. And it's not the same as the book. Is the book wrong or i am ?
 
  • #4
1,137
0
I need to sleep now ... its 3AM here ...

But you can post your answer and i'll tell you your mistake as soon as i wake up.
will that work?
 
  • #5
81
1
of course, no hurry:smile:

You can find my answer in the point 3 of my first post

thanks
 

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