$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

$A$ bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10 \text{ m}$. $A$ point mass $A$ of mass $m$ travelling horizontally with speed $10 \text{ ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meters after the collision. Taking the acceleration due to gravity $g = 10 \text{ ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

$A$ bullet of mass $0.01 \, kg$ travelling at a speed of $500 \, m/s$ strikes a block of mass $2 \, kg$ which is suspended by a string of length $5 \, m$. The center of gravity of the block is found to rise a vertical distance of $0.1 \, m$. What is the speed of the bullet after it emerges from the block?

$A$ man of mass $60 \ kg$ gets $10^5 \ calories$ of energy from food. If his efficiency is $28\%$,up to what height in $m$ can he climb?

The mass of a person is $60 \, kg$. If he gains $10^5 \, \text{calories}$ of heat energy from food and the efficiency of his body is $28 \%$,then up to what height can he climb? (approximately) ($g = 9.8 \, m/s^2$,$J = 4.2 \, J/\text{cal}$)