$A$ spaceship of speed $v_0$ travelling along $+y$ axis suddenly shoots out one-fourth of its part with speed $2v_0$ along $+x$ axis. The $xy$ axes are fixed with respect to the ground. The velocity of the remaining part is:

$A$ ball of mass $m$ is moving towards a wall with velocity $v$ at an angle $\theta$ with the normal to the wall, as shown in the diagram. In which direction is its linear momentum conserved?

$A$ bomb of mass $9 \text{ kg}$ explodes into two pieces of mass $3 \text{ kg}$ and $6 \text{ kg}$. The velocity of mass $3 \text{ kg}$ is $16 \text{ m/s}$. The kinetic energy of mass $6 \text{ kg}$ (in joule) is

$A$ projectile of mass $m$ is projected from ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle comes to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground is: (in $, m$)

If the resultant of all the external forces acting on a system of particles is zero,then from an inertial frame,one can surely say that

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with $u_{rel}$ with respect to the trolley,then the velocity of the trolley is