Block $A$ of mass $m$ is hanging from a vertical spring of spring constant $k$ and is at rest. Block $B$ of mass $m$ strikes block $A$ with velocity $v$ and sticks to it. The velocity $v$ for which the spring just attains its natural length is:

$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is:

By how much should the spring be compressed by the block so that the centripetal force at point $P$ is $mg$?

In a one-dimensional collision between two particles,their relative velocity is $\vec{v}_1$ before the collision and $\vec{v}_2$ after the collision.

Two cars,both of mass $m$,collide and stick together. Prior to the collision,one car had been traveling north at speed $2v$,while the second was traveling at speed $v$ at an angle $\phi$ south of east (as indicated in the figure). The magnitude of the velocity of the two-car system immediately after the collision is:

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass $1.00 \; g$ falling from a height $1.00 \; km$. It hits the ground with a speed of $50.0 \; m s^{-1}$. $(a)$ What is the work done by the gravitational force? $(b)$ What is the work done by the unknown resistive force?