$A$ man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun has a mass of $1 \,kg$. With what velocity does the gun recoil backwards?

$A$ cat with mass $m_c$ is sitting at rest on the left plank of a pair of identical planks. Each plank has mass $m_s$ and they rest on frictionless ice. Suddenly,the cat leaps to the right plank,traveling with a horizontal speed $v_{cg}$ measured with respect to the ground. The instant the cat reaches the right plank,it turns around and leaps back to the left plank. The horizontal component of the cat's speed is again $v_{cg}$ measured with respect to the ground. The final speed of the right plank in terms of the masses of the cat and planks and the cat's leaping speed is (The cat remains on the left plank after its return).

$A$ body of mass $5 \ kg$ initially at rest explodes into three fragments. The ratio of the masses of the three fragments is $1 : 1 : 3$. The two fragments of equal mass move in mutually perpendicular directions with a velocity of $21 \ m/s$. What is the velocity of the heaviest fragment in $m/s$?

$A$ bomb of mass $16 \,kg$ explodes into two pieces of masses $4 \,kg$ and $12 \,kg$. The velocity of the $12 \,kg$ mass is $4 \,ms^{-1}$. The kinetic energy of the second piece (the $4 \,kg$ piece) is: (in $\,J$)

$A$ bullet of mass $0.1\,kg$ is fired with a speed of $100\,m/s$. The mass of the gun is $50\,kg$. The recoil velocity of the gun is ........ $m/s$.

Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?