Question

A man weighing $80kg$ is standing at the centre of a flat boat and he is $20m$ from the shore. He walks $8m$ on the boat towards the shore and then halts. The boat weighs $200kg$. How far is he from the shore at the end of this time?

• A. $11.2m$
• B. $13.8m$
• C. $14.3m$
• D. $15.4m$

Answer 1

Answer: (C)

$14.3m$

Initial position of boat ,$x_{bi}=20m$
Initial position of man ,$x_{mi}=20m$
Let the final position of boat $=x_{bf}$
so the final position of man ,$x_{mf}=x_{bf}-8$
Since the man+boat system was initially at rest, then the system stays at rest, and therefore the center of mass of the system does not change.Thus,

$\frac{m_b{x}_{bi}+m_m{x}_{mi}}{m_b+m_m}=\frac{m_b{x}_{bf}+m_m{x}_{mf}}{m_b+m_m}$

or, $200\left(20\right)+80\left(20\right)=200\left(x_{bf}\right)+80(x_{bf}-8)$.
or, $4000+1600=280x_{bf}-640$

or,$x_{bf}=\frac{6240}{280}=22.28m$

Thus the final position of the man from shore ,$x_{mf}=22.28-8=14.3m$