A rigid rod $$(AB)$$ of length $$L = \sqrt 2 $$ m is undergoing translational as well as rotational motion in the $$ x-y$$ plane (see the figure). The point $$A$$ has the velocity $${V_1} = \widehat i + 2\widehat jm/s.$$ The end $$B$$ is constrained to move only along the $x$$ direction.

The magnitude of the velocity $${V_2}$$ (in $$m/s$$) at the end $$B$ is __________

A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $$0.25.$$ The string can withstand a maximum force of $$20$$ N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ____________ kg.
Take $$\cos \theta = 0.8$$ and $$\sin \theta = 0.6$$. Acceleration due to gravity g $$=$$ $$10$$ m/s²

A two-member truss $$PQR$$ is supporting a load W. The axial forces in members $$PQ$$ and $$QR$$ are respectively

The initial velocity of an object is $$40$$ $$m/s.$$ The acceleration a of the object is given by the following expression: a$$=-0.1v$$
Where v is the instantaneous velocity of the object. The velocity of the object after $$3$$ seconds will be _______