$A$ man (mass $= 50\, kg$) and his son (mass $= 20\, kg$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is ........ $ms^{-1}$

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then

$A$ stationary body of mass $m$ explodes into $3$ parts having masses in the ratio $1 : 3 : 3$. The two parts having equal mass move at right angles to each other with a velocity of $15\,m/s$. What is the velocity of the third part?

$A$ body,whose momentum is constant,must have constant

$A$ cat with mass $m_c$ is sitting at rest on the left plank of a pair of identical planks. Each plank has mass $m_s$ and they rest on frictionless ice. Suddenly,the cat leaps to the right plank,traveling with a horizontal speed $v_{cg}$ measured with respect to the ground. The instant the cat reaches the right plank,it turns around and leaps back to the left plank. The horizontal component of the cat's speed is again $v_{cg}$ measured with respect to the ground. The final speed of the right plank in terms of the masses of the cat and planks and the cat's leaping speed is (The cat remains on the left plank after its return).

$A$ projectile is moving at $20 \, m/s$ at its highest point,where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30 \, m/s$. Then the other part will move at ............. $m/s$.