A 750 kg boat is 10 m long and is floating | vedclass

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(B) Mass of the boat,$M = 750 \ kg$. Mass of the man,$m = 80 \ kg$. Length of the boat,$L = 10 \ m$. Since there is no external horizontal force actin

Vedclass · Accepted Answer

$0.96 \ m$ in the direction opposite to the displacement of the man

Vedclass · Answer

(B) Mass of the boat,$M = 750 \ kg$. Mass of the man,$m = 80 \ kg$. Length of the boat,$L = 10 \ m$. Since there is no external horizontal force acting on the system (boat + man),the centre of mass of the system remains stationary. Let the boat displace by a distance $x$ in the direction opposite to the man's motion. The man moves a distance $L$ relative to the boat,so his displacement relative to the water is $(L - x)$. The displacement of the boat's centre of mass relative to the water is $x$ in the opposite direction. Using the principle of conservation of the centre of mass: $m \Delta x_m + M \Delta x_B = 0$. Here,$\Delta x_m = (L - x)$ and $\Delta x_B = -x$. Substituting the values: $80(10 - x) + 750(-x) = 0$. $800 - 80x - 750x = 0$. $830x = 800$. $x = \frac{800}{830} \approx 0.96 \ m$. Thus,the boat moves $0.96 \ m$ in the direction opposite to the man's displacement.

$A$ $750 \ kg$ boat is $10 \ m$ long and is floating without motion on still water. $A$ man of mass $80 \ kg$ is at one end. If he runs to the other end of the boat and stops,the displacement of the boat is:

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