In which direction do the following forces act when an object is in motion?
$(i)$ Frictional force
$(ii)$ Gravitational force
$(iii)$ Centripetal force

$(i)$ Define momentum. Write its $SI$ unit.
$(ii)$ How much momentum will an object of mass $10 \ kg$ transfer to the floor if it falls from a height of $5 \ m$? $(g = 10 \ m \ s^{-2})$
$(iii)$ Explain how a karate player can break a pile of tiles with a single blow of his hand.

State whether the following statement is true or false:
Impulse represents the rate of change of momentum of a body.

Quick sand consists of very smooth and tiny grains of sand. What would happen if a man or a heavy animal steps over a patch of such sand in a desert?

What would be the force required to stop a car of mass $1000 \ kg$ and a loaded truck of mass $10000 \ kg$ in $2 \ s$,if they are moving with the same velocity of $5 \ m s^{-1}$?

$(a)$ State the law of conservation of momentum.
$(b)$ Mention two factors which determine the momentum of a body.
$(c)$ Prove the law of conservation of momentum with clear explanation,diagram and equation.