Centre of Mass & Collisions

A rocket of initial mass 1000 kg burns fuel at 5 kg/s and ejects it at 2000 m/s relative to itself. Find its speed 40 s after launch, ignoring gravity.

Two identical balls undergo an oblique elastic collision, with one initially at rest. If one ball moves off at 40° after the collision, find the angle of the other.

A uniform chain (linear density 1 kg/m) falls from rest, held vertically with its lower end at the floor. Find the normal reaction on the pile when it has fallen 3 m and the falling end moves at 5 m/s. (g = 10 m/s²)

A bomb at rest splits into two fragments of mass 4 kg and 6 kg. The 4 kg piece moves at 9 m/s. Find the speed of the 6 kg piece.

A ball dropped from 8 m bounces back to a height of 2 m. Find the coefficient of restitution.

A 1 kg ball moving at 9 m/s collides elastically head-on with a stationary 2 kg ball. Find the velocity of the 1 kg ball after collision.

A 3 kg ball moving at 12 m/s collides perfectly inelastically with a stationary 9 kg ball. Find their common velocity after collision.

A 2 kg particle moves with velocity (3,0) m/s and a 3 kg particle moves with velocity (0,4) m/s. Find the velocity of their centre of mass.

A 2 kg ball moving at 10 m/s collides perfectly inelastically with a stationary 3 kg ball. Find the kinetic energy lost in the collision.

A 0.5 kg ball hits a wall at 10 m/s and rebounds with coefficient of restitution 0.6. Find the impulse delivered by the wall.

A rocket (ignore gravity) has initial mass 500 kg and final mass 100 kg, ejecting fuel at 1500 m/s relative to itself. Find its final speed (starting from rest).

Two 5 kg balls move toward each other, one at 4 m/s and the other at 2 m/s (opposite direction). They collide and stick together. Find their common velocity after collision.