$A$ bomb at rest in the air explodes into two fragments. If one fragment moves vertically upwards with a velocity $v_0$,in which direction will the other fragment move?

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

$A$ man weighing $80 \, kg$ is standing in a trolley weighing $320 \, kg$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of $1 \, m/s$ relative to the trolley,then after $4 \, s$ his displacement relative to the ground will be ........ $m$.

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 the person standing at $A$ jumps from the trolley towards the left with $u_{rel}$ with respect to the trolley,then:

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

$A$ body of mass $1 \,kg$, initially at rest, explodes and breaks into three parts. The masses of the parts are in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed of $30 \,m/s$ each. The velocity of the heavier part in $m/s$ is