A cart loaded with sand moving with velocity $v$. Sand is falling through the hole as shown in diagram then after falling on the ground sand is

A shell of mass $m$ moving with velocity $ v$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be

A wagon weighing $1000\, kg$ is moving with a velocity $50\,km/h$ on smooth horizontal rails. A mass of $250 \,kg$ is dropped into it. The velocity with which it moves now is ......... $km/hour$

A mass $m$ moving horizontally (along the $x-$ axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$ axis) with velocity $2v$. The final velocity of the combination is

A man is standing at the centre of frictionless pond of ice. How can he get himself to the shore

A projectile is fired with velocity $u$ at an angle $\theta$ with horizontal. At the highest point of its trajectory it splits up into three segments of masses $m, m$ and $2 \,m$. First part falls vertically downward with zero initial velocity and second part returns via same path to the point of projection. The velocity of third part of mass $2 \,m$ just after explosion will be