$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is: (in $ms^{-1}$)

$A$ spacecraft of mass $M$ is moving in space with a velocity $v$. It explodes and breaks into two pieces. After the explosion,a piece of mass $m$ comes to rest. The velocity of the other piece is ......

In a gravity-free space,a man of mass $M$ standing at a height $h$ above the floor,throws a ball of mass $m$ straight down with a speed $u$. When the ball reaches the floor,the distance of the man above the floor will be

$A$ shell at rest at the origin explodes into three fragments of masses $1 \ kg$,$2 \ kg$,and $m \ kg$. The $1 \ kg$ and $2 \ kg$ pieces fly off with speeds of $5 \ m/s$ along the $x$-axis and $6 \ m/s$ along the $y$-axis,respectively. If the $m \ kg$ piece flies off with a speed of $6.5 \ m/s$,the total mass of the shell must be ......... $kg$.

$A$ man of $60\,kg$ is running on the road and suddenly jumps into a stationary trolley car of mass $120\,kg$. Then,the trolley car starts moving with a velocity of $2\,ms^{-1}$. The velocity of the running man when he jumped into the car was . . . . . . $ms^{-1}$.

$A$ $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m/s$ and $Q$ with speed $40 \,m/s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about (in $^{\circ}$)