Let mass of bullet be $m_1=20g$
Let mass of the wooden block be $m_2=80g$
Let initial velocity of the bullet be $u_1$ = $100m{s}^{-1}$ and final velocity of the bullet be $v_1$.
Let the initial velocity of wooden block be $u_2$, since it was at rest, the initial velocity is zero, i.e  $u_2=0m{s}^{-1}$
Let final velocity of the wooden block be $v_2$.
By applying law of conservation of momentum,
intial momentum of the system = final momentum of the system
i.e, $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$
After the bullet is fired, the bullet gets embedded on the block.
Therefore, it acts as a system
Hence , the final velocity of the bullet and wooden block after collision will be equal as it works as a system
i.e $v_1=v_2=v$ where v is the velocity of the system after collision.
Substituting on the equation, we get 
$(0.020\times 100)+(0.080\times 0)=v\times (0.020+0.080)$
$\Rightarrow$ $2=0.1\times v$
$\Rightarrow$ $v=20{ms}^{-1}$​

$\therefore$Velocity of system after collision  = $20{ms}^{-1}$​

According to newton's second law of motion-"the rate of change of momentum is directly proportional to force applied and the change in momentum is in the direction of force applied." Newton's second law of motion gives mathematical expression of force.
Force $\propto$ $\frac{dp}{dt}$

The weight of the object exerts a force on the table. The table in return exerts a reaction force which is equal to the magnitude of the weight and opposite in direction (Newton's third law). Thus, the net force on the object is zero as two equal forces in opposite directions are acting on it and hence the object remains at rest.
 

Newton's second law states that the rate of change of momentum of an object is directly proportional to the net force acting on it, provided that the mass of the body is kept constant. It gives the mathematical expression of force.

Newton's second law of motion gives us the quantitative analysis of force. It gives us the mathematical expression of force as it states that  the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.

Initial velocity of the stone = $20m{s}^{-1}$.
Final velocity of the stone, $v=0$(finally the stone comes to rest).
Distance covered by the stone = 50 m.
According to third equation of motion:
$v^2=u^2+2as$
0 × 0 = 20 × 20 + 2 × a × 50
$\Rightarrow$$a=-4m{s}^{-2}$.
The negative sign indicates that acceleration is in the opposite direction to the motion of  the stone.
Mass of the stone, $m=1kg$.
From the newton's second law of motion:
Force = mass × acceleration. Therefore,
$F=1\times -4=-4N$.
Hence, the force of friction between the stone and the ice is 4N. The negative sign indicates that friction oppposes the relative motion.

Newton's first law states that an object at rest stays at rest and an object in motion stays in motion unless acted upon by an unbalanced force. This is also called the law of inertia because inertia is the property of any object by virtue of which it retains its state of motion. The importance of Newton's first law of motion also lies in the fact that it mentions force and gives us a qualitative idea about it.