Explanation:
We assume that length of boat is L cm. And, we suppose to have a coordinate system relative to the bottom of the lake with:
Boat's position initially from x = 0 cm to x = L cm
Let person (S) is initially at x = L cm (right hand end of boat)
and, let boat's center of mass at x = C cm
Therefore, initially center of mass of overall (system's) is at where (taking moments about x = 0).
= 130C + 80L ........... (i)
After S walks left to the other end of the boat, the boat moves right 80 cm.
Hence,
Boat's position is now from x = 80 cm to x = (L+ 80) cm
S's position is x = 80 (left end of boat)
Boat's center of mass is at (C + 80).
Therefore, overall (system's) final center of mass is at where (taking moments about x = 0).
= ............. (ii)
As no external force is acted on the system, the system's center of mass has not moved, so .
This means the left hand sides of both equations (i) and (ii) are equal. So, we can equate the right hand sides giving: the equation as follows.
130C + 80L =
80L = 16800 cm
L = 210 cm
= 2.1 m
Length of boat = 2.1 m
When the person is walking from one end to the other as there was no external force then center of mass of the person-boat system did not move.