Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

$A$ 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).

$A$ $1 \; kg$ stationary bomb explodes into three parts having mass ratio $1:1:3$. The parts with equal mass move in perpendicular directions with a velocity of $30 \; m/s$. What is the velocity of the third (heavier) part?

Three particles of masses $10\;g, 20\;g$ and $40\;g$ are moving with velocities $10\hat{i}, 10\hat{j}$ and $10\hat{k}\;m/s$ respectively. If due to some mutual interaction,the first particle comes to rest and the velocity of the second particle becomes $(3\hat{i} + 4\hat{j})\;m/s$,then the velocity of the third particle is

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of the other part will be

$A$ bomb of mass $3.0 \, kg$ explodes in air into two pieces of masses $2.0 \, kg$ and $1.0 \, kg$. The smaller mass travels at a speed of $80 \, m/s$. The total energy imparted to the two fragments is ............. $kJ$.