Prove that in a two dimensional elastic collision of a moving ball with another stationary identical ball, the two balls move perpendicular to each other after collision?

In an elastic collision between smooth balls :

A ball of mass m makes an elastic collision with another identical ball at rest. Show that if the collision is oblique, the bodies go at right angles to each other after collision.

Consider an oblique elastic collision between a moving ball and a stationary ball of the same mass. Both the balls move with the same speed after the collision. After the collision, the angle between the directions of motion of two balls is x degree. Find the value of x.

A ball of mass m moving with velocity v collides head on elastically with another identical ball moving with velocity - V. After collision

A ball of mass m moving with velocity V , makes a head on elastic collision with a ball of the same moving with velocity 2 V towards it. Taking direction of V as positive velocities of the two balls after collision are.

Two identical particles move --------- to eachother after elastic collision in two dimensions.

A ball moving on a horizontal frictionless plane hits an identical ball at rest with a velocity of 0.5m//s . If the collision is elastic, calculate the speed imparted to the target ball, if the speed of projectile after the collision is 30cm//s . Show that the two balls will move at right angles to eachother, after the collision.

A billiard ball collides elastically with an identical stationary ball. The collision is not head on. Show that the directions of motion of the two balls are at right angles after the collision. Solve the problem in centre of mass frame as well as in lab frame.