$A$ 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 $10 \, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $X$-axis,hits another ball of mass $20 \, kg$ which is at rest. After the collision,the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along the $Y$-axis at a speed of $10 \, m/s$. The second piece starts moving at a speed of $20 \, m/s$ at an angle $\theta$ (in degrees) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$ to the nearest integer is:

$A$ bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{i}$ and $p \hat{j}$,find the magnitude of momentum of the third part.

$A$ 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:

$A$ shell of mass $20 \,kg$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$. The smaller fragment moves with a velocity of $6 \,ms^{-1}$. The kinetic energy of the larger fragment is (in $\,J$)

$A$ bullet of mass $40 \,g$ is fired from a gun of mass $10 \,kg$. If the velocity of the bullet is $400 \,m/s$,then the recoil velocity of the gun will be ..........