In the given figure, the acceleration of $A$ is $\overrightarrow{a_A}=15\hat{\mathrm{i}}+15\hat{\mathrm{j}}$. Then the acceleration of $B$ is ($A$ remains in contact with $B$)

In the given figure, the mass $m_2$ starts with velocity $v_0$ and moves with constant velocity on the surface. During motion, the normal reaction between the horizontal surface and fixed triangle block $m_1$ is $N$. Then during motion 

In the given figure, blocks $A$ and $B$ move with velocities $v_1$ and $v_2$ along horizontal direction. Find the ratio of $\frac{v_1}{v_2}$.

If block $B$ moves towards right with acceleration $b$, find the net acceleration of block $A$.

If the blocks $A$ and $B$ are moving towards each other with accelerations $a$ and $b$ as shown in figure, then find the net acceleration of block $C$. 

A block $A$ has a velocity of $0.6 \mathrm{m} {\mathrm{s}}^{-1}$ to the right. Determine the velocity of cylinder $B$. 

For the pulley system shown in figure, each of the cables at $A$ and $B$ is given a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ in the direction of the arrow. Determine the upward velocity $v$ of the load $m$.

In the following arrangement, the system is initially at rest. The $5-\mathrm{kg}$ block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of block $C$ will be