$A$ ball of mass $0.5 \ kg$ is dropped from a height of $40 \ m$. The ball hits the ground and rises to a height of $10 \ m$. The impulse imparted to the ball during its collision with the ground is (Take $g = 9.8 \ m/s^2$)

$A$ ball of mass $0.15 \; kg$ hits the wall with an initial speed of $12 \; m/s$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $100 \; N$,calculate the time duration of the contact of the ball with the wall in seconds.

$A$ machine gun can fire $200$ bullets $\min^{-1}$. If $35 \ g$ bullets are fired at a speed of $750 \ m \ s^{-1}$,the average force exerted by the gun on the bullets is, (in $N$)

$A$ force is applied to a body of mass $2 \,kg$ at rest on a frictionless horizontal surface, as shown in the force-time $(F-t)$ graph. The speed of the body after $1 \,s$ is: (in $\,m/s$)

$A$ batsman hits back a ball of mass $0.4 \; kg$ straight in the direction of the bowler without changing its initial speed of $15 \; ms^{-1}$. The impulse imparted to the ball is $\dots \; Ns$.

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