The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys as shown in the figure. Calculate the time taken by the box of mass $8\, {kg}$ to strike the ground starting from rest. (Use $g = 10\, {m/s^2}$) (in ${s}$)

$A$ rod is constrained to move along a vertical wall and a horizontal floor. If the velocity of end $A$ is $V_A$ along the horizontal floor,find the velocity $V_B$ of end $B$ along the vertical wall in terms of $V_A$ and $\theta$.

$A$ basket and its contents have mass $M$. $A$ monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2 \, ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3 \, s$. How fast is the basket rising at the end of the $3 \, s$? Neglect the mass of the pulley and the rope. (given : $g = 32 \, ft/s^2$)

If block $A$ is moving with an acceleration of $5\,m/s^2$,the acceleration of $B$ with respect to the ground is:

In the arrangement shown in the figure,the ends $P$ and $Q$ of an unstretchable string move downwards with a uniform speed $U$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upwards with a speed:

If the acceleration of block $A$ is $2\,m/s^2$ to the left and the acceleration of block $B$ is $1\,m/s^2$ to the left, then find the acceleration of block $C$.