A ball is thrown vertically downwards from a height of 20 m with an initial velocity v₀. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v₀ is
(Take g = 10 m s^$$-$$2)

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $$\theta $$ to its initial direction and has a speed $${v \over 3}.$$ The second block's speed after the collision is

A block of mass 10 kg, moving in x direction with a constant speed of 10 m s^$$-$$1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is