Two billiard balls of equal mass $30 \, g$ strike a rigid wall with the same speed of $108 \, km/h$ (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball $'a'$ and ball $'b'$ by the wall along the $'X'$ direction is:

The momentum $p$ of an object varies with time $(t)$ as shown in the figure. The corresponding force $(F)$-time $(t)$ graph is

Three different projectiles,each with the same mass $m$,are fired with speed $v$ at a wall. In case $A$,the projectile bounces straight back with speed $v$. In case $B$,the projectile sticks to the wall. In case $C$,the projectile crashes through the wall and emerges with half its original speed. These three cases are shown in the figure. Place the magnitude of the impulse exerted by the wall on the projectile in each of these three cases in the correct order.

$A$ batsman deflects a ball by an angle of $45^{\circ}$ without changing its initial speed,which is equal to $54 \; km/h$. What is the impulse imparted to the ball in $kg \; m/s$? (Mass of the ball is $0.15 \; kg$.)

$A$ boy hits a baseball with a bat and imparts an impulse $J$ to the ball. The boy hits the ball again with the same force,except that the ball and the bat are in contact for twice the amount of time as in the first hit. The new impulse equals:

$A$ mass of $100\,g$ strikes the wall with a speed of $5\,m/s$ at an angle as shown in the figure and it rebounds with the same speed. If the contact time is $2 \times 10^{-3}\,s$,what is the force applied on the mass by the wall?