An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ is the mass per unit length of the water jet. If this jet hits a surface and comes to rest instantaneously,the force on the surface is

$A$ machine gun fires $20$ bullets per second into a target. Each bullet weighs $150 \, g$ and has a speed of $800 \, m/s$. Find the force necessary to hold the gun in position.

$A$ solid horizontal surface is covered with a thin layer of oil. $A$ rectangular block of mass $m = 0.4 \ kg$ is at rest on this surface. An impulse of $1.0 \ N \ s$ is applied to the block at time $t = 0$ so that it starts moving along the $x$-axis with a velocity $v(t) = v_0 e^{-t/\tau}$,where $v_0$ is a constant and $\tau = 4 \ s$. The displacement of the block,in metres,at $t = \tau$ is. . . . . . . Take $e^{-1} = 0.37$.

$A$ 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:

If the final momentum is equal to the initial momentum of the system,then: