$A$ hammer of mass $500 \,g$,moving at $50 \,m/s$,strikes a nail. The nail stops the hammer in a very short time of $0.01 \,s$. What is the force (in $N$) of the nail on the hammer?

From a rifle of mass $4\, kg$,a bullet of mass $50\, g$ is fired with an initial velocity of $35\, m\, s^{-1}$. Calculate the initial recoil velocity (in $m/s$) of the rifle.

Why is it advised to tie any luggage kept on the roof of a bus with a rope?

$A$ bullet of mass $10\, g$ travelling horizontally with a velocity of $150\, m/s$ strikes a stationary wooden block and comes to rest in $0.03\, s$. Calculate the distance of penetration of the bullet into the block. Also,calculate the magnitude of the force exerted by the wooden block on the bullet.

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Two objects of masses $100 \, g$ and $200 \, g$ are moving along the same line and direction with velocities of $2 \, m \, s^{-1}$ and $1 \, m \, s^{-1}$,respectively. They collide and after the collision,the first object moves at a velocity of $1.67 \, m \, s^{-1}$. Determine the velocity (in $m/s$) of the second object.