$A$ cart of mass $M$ is tied to one end of a massless rope of length $10\, m$. The other end of the rope is held by a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $x = 0$ and the cart is at $x = 10\, m$. If the man pulls the cart by the rope,the man and the cart will meet at the point:

Two particles of masses $1 \,g$ and $2 \,g$ move towards each other with velocities $10 \,ms^{-1}$ and $20 \,ms^{-1}$ respectively. The velocity of the centre of mass of the system of the two particles is (in $\,ms^{-1}$)

$A$ man of mass $m$ is suspended in air by holding the rope of a balloon of mass $M$. As the man climbs up the rope,the balloon

$A$ block of mass $M$ is tied to one end of a massless rope. The other end of the rope is in the hands of a man of mass $2M$ as shown in the figure. Initially,the block and the man are resting on a rough plank of mass $2M$ as shown in the figure. The whole system is resting on a smooth horizontal surface. The man pulls the rope. The pulley is massless and frictionless. What is the magnitude of the displacement of the plank when the block meets the pulley? (The man does not leave his position on the plank during the pull).

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

Explain translational motion by the given illustration.