An athlete always runs some distance before taking a jump. Why?

$(a)$ State the law of conservation of momentum.
$(b)$ $A$ body of mass $2 \, kg$,initially moving with a velocity of $10 \, m s^{-1}$,collides with another body of mass $5 \, kg$ at rest. After the collision,the velocity of the first body becomes $1 \, m s^{-1}$. Find the velocity of the second body.

$A$ man pushes a box of mass $50\, kg$ with a force of $80\, N$. What will be the acceleration of the box due to this force? What would be the acceleration if the mass were doubled?

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 $5 \ m s^{-1}$?

Two forces $F_{1} = 20 \, N$ and $F_{2} = 30 \, N$ are acting on an object in opposite directions as shown in the figure.
$(i)$ What is the net force acting on the object?
$(ii)$ What is the direction of the net force acting on the object?
$(iii)$ If the mass of the body is $10 \, kg$,what will be the acceleration produced in it?

$(a)$ 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.