Question

A striped billiard ball moves toward the right with speed 3 m/s. A solid billiard ball with the same mass moves toward the left at the same speed. The two balls collide head on, causing each ball to reverse its direction of motion. If the collision is elastic, what is the final speed of the striped ball in m/s

Answer 1

Answer:

Final speed of striped ball is 3 m/s in left direction .

Explanation:

Given :

Two billiard ball with the same mass moves toward the left at the same speed 3 m/s .

Let , us assume right hand side direction to be positive and left hand side direction to be negative .

Also , let speed of ball after collision is (striped ball ) u and (solid ball) v .

It is also given that the collision is elastic .

Therefore , kinetic energy is conserved .

$\dfrac{m(3)^2}{2}+\dfrac{m(3)^2}{2}=\dfrac{mu^2}{2}+\dfrac{mv^2}{2}\\\\u^2+v^2=18$ ...... ( 1 )

Also , by conserving linear momentum .

We get :

$3m-3m=mu+mv\\u=-v$                ...... ( 2 )

Putting value of u from equation 2 to equation 1 .

We get :

$2v^2=18\\v=3\ m/s$

And , u = -3 m/s .

Therefore , final speed of striped ball is 3 m/s in left direction .

Hence , this is the required solution .