A 500 kg boat is 9 m long and is floating without motion on still water. A man of mass 100 kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

Question

A 500 kg boat is 9 m long and is floating without motion on still water. A man of mass 100 kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is (A) 1.5 m in the direction of displacement of the man (B) 0.75 m in the direction of displacement of the man (C) 1.5 m in the direction opposite to the displacement of the man (D) 0.75 m in the direction opposite to the displacement of the man

Tardigrade Admin · Accepted Answer

Given that the system is initially at rest,
i. e. ,

v_{CM} = 0

∴ \frac{m _{1} v _{1} + m _{2} v _{2}}{m _{1} + m _{2}} = 0

m_{1} v_{1} + m_{2} v_{2} = 0

m_{1} \frac{Δ r _{1}}{Δ t} + m_{2} \frac{Δ r _{2}}{Δ , t} = 0

m_{1} Δ r_{1} + m_{2} r_{2} = 0

Now here, in boat-man system, if the man moves towards right the boat moves toward left

m_{1} Δ r_{1} \pm m_{2} Δ r_{2}

If

Δ r_{2}

is the displacement of boat relative to shore; there the displacement of man relative to shore would be

(9 - Δ r_{2})

Δ r_{1} = 9 - Δ r_{2}

m_{1} (9 - Δ r_{2}) = m_{2} Δ r_{2}

100 (9 - Δ r_{2}) = 500 Δ r_{2}

Δ r_{2} = \frac{100 \times 9}{600} = 1.5 m

i. e. , Boat moves

1.5 m

relative to shore in the direction opposite to the displacement of man.

Q. A 500kg boat is 9m long and is floating without motion on still water. A man of mass 100kg is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is

1.5 m in the direction of displacement of the man

0.75 m in the direction of displacement of the man

1.5 m in the direction opposite to the displacement of the man

0.75 m in the direction opposite to the displacement of the man

Q. A $500 k g$ boat is $9 m$ long and is floating without motion on still water. A man of mass $100 k g$ is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is