$A$ cannon after firing recoils due to

The average force necessary to stop a hammer with momentum $p \; Ns$ in $0.5 \; s$ is .......... $N$.

$A$ small mass $m$ is launched from the top of a cliff with speed $V$ at an angle of $30^{\circ}$ above the horizontal. When the mass reaches the ground,its velocity is directed at $45^{\circ}$ below the horizontal. Which one of the following choices is the magnitude of the total impulse that was imparted to the mass during its flight? Ignore air resistance.

$A$ particle moves in the $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{P}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$. If $k$ is a constant,the angle between $\vec{F}$ and $\vec{P}$ will be:

$A$ particle of mass $m$,initially at rest,is acted on by a force $F = F_0 \left\{ {1 - {{\left( {\frac{{2t - T}}{T}} \right)}^2}} \right\}$ during the interval $0 \leq t \leq T$. The velocity of the particle at the end of the interval is:

In an hour-glass,approximately $100$ grains of sand fall per second (starting from rest); and it takes $2 \, s$ for each sand particle to reach the bottom of the hour-glass. If the average mass of each sand particle is $0.2 \, g$,then the average force exerted by the falling sand on the bottom of the hour-glass is close to .......... $N$.