$A$ girl of mass $50 \, kg$ jumps out of a moving boat of mass $300 \, kg$ onto the bank with a horizontal velocity of $3 \, m s^{-1}$. With what velocity will the boat begin to move backwards (in $, m s^{-1}$)?

$(a)$ How much momentum will an object of mass $10 \ kg$ transfer to the floor if it falls from a height of $0.8 \ m$? $(g = 10 \ m s^{-2})$
$(b)$ Explain why it is difficult for a fireman to hold a hose,which ejects a large amount of water at a high velocity.

$A$ bullet of mass $5 \, g$ travelling at a speed of $120 \, m s^{-1}$ penetrates deeply into a fixed target and is brought to rest in $0.01 \, s$. Calculate: $(a)$ the distance of penetration in the target,$(b)$ the average force exerted on the bullet.

$(a)$ $(i)$ Define momentum. State its $SI$ unit.
$(ii)$ An object of mass $50 \ kg$ is accelerated uniformly from a velocity of $4 \ m/s$ to $8 \ m/s$ in $8 \ s$. Find the magnitude of the force exerted on the object.
$(b)$ State Newton's first law of motion.

$A$ body of mass $500 \, g$ is at rest on a frictionless surface. Calculate the distance travelled by it in $10 \, s$ when acted upon by a force of $10^{-2} \, N$. (in $, m$)

Name and state the action and reaction in the following cases:
$(i)$ Firing of a bullet from a gun.
$(ii)$ Hammering a nail.
$(iii)$ $A$ book lying on a table.
$(iv)$ Moving rocket.
$(v)$ $A$ person moving on the floor.
$(vi)$ $A$ moving train colliding with a stationary train.