Two particles A and B, move with constant velocities $$\overrightarrow {{v_1}} $$ and $$\overrightarrow {{v_2}} $$. At the initial moment their position vectors are $$\overrightarrow {{r_1}} $$ and $$\overrightarrow {{r_2}} $$ respectively. The condition for particles A and B for their collision is

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 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)

Two similar springs P and Q have spring constants K_P and K_Q, such that K_P > K_Q. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs W_P and W_Q are related as, in case (a) and case (b) respectively