$A$ 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 $0.15 \; kg$.)

$A$ soccer ball of mass $250 \text{ g}$ is moving horizontally to the left with a speed $22 \text{ ms}^{-1}$. This ball is kicked towards the right with a velocity $30 \text{ ms}^{-1}$ at an angle $53^{\circ}$ with the horizontal in the upward direction. Assuming that it took $0.01 \text{ s}$ for the collision to take place, the average force acting is $(\cos 53^{\circ} = \frac{3}{5}; \sin 53^{\circ} = \frac{4}{5})$. (in $\text{ N}$)

$A$ particle of mass $m$ strikes elastically on a wall with velocity $v$,at an angle of $60^{\circ}$ from the wall. The magnitude of the change in momentum of the particle along the wall is:

$A$ particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{P}$ at any time $t$ is $P_x = 2\cos t$ and $P_y = 2\sin t$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be $\theta = $ ........... $^o$.

In the figure,the position-time graph of a particle of mass $0.1\, kg$ is shown. The impulse at $t = 2\, s$ is ......... $kg\, m/s$.

Two balls each of mass $250 \ g$ moving in opposite directions each with a speed $16 \ m \ s^{-1}$ collide and rebound with the same speeds. The impulse imparted to one ball due to the other is