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

A shell is fired from a cannon with velocity $v m/sec$ at an angle $\theta $ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in $m/sec $ of the other piece immediately after the explosion is

A mass of $100\,g$ strikes the wall with speed $5\,m/s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 \times {10^{ - 3}}\,\sec $, what is the force applied on the mass by the wall

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Figure. What is

$(i)$ the direction of the force on the wall due to each ball?

$(ii)$ the ratio of the magnitudes of impulses imparted to the balls by the wall ?

A bullet of mass $50$ gram is fired from a $5 \,kg$ gun with a velocity of $1km/s$. the speed of recoil of the gun is .......... $m/s$

A man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun is of one $kg$ mass. by what velocity the gun rebounds backwards ........ $m/s$