What Happens to Billiards Balls in an Elastic Collision at Right Angles?

[mitchmcsscm94]

Homework Statement

Two billiards balls of equal mass move at right angles and meet at the origin of an xy coordinate system. One is moving upward along the y-axis at 2.0 m/s, and the other is moving to the right along the x-axis with speed 3.7 m/s. After the collision( assumed elastic), the second ball is moving along the positive y axis. What is the final direction of the first ball, and what are the two speeds?

Homework Equations

it is elastic so
P₁+P₂=P₁final+P₂final
mass is constant so it cancels
V₁+V₂=V₁final+V₂final

The Attempt at a Solution

i got 5.7=V₁final+V₂final

 

[Nytik]

A couple of things that might help:

Since the collision is elastic, kinetic energy is conserved.
The problem is in two dimensions! Remember momentum is a vector quantity. (Can you just add the initial velocities to give 5.7ms^-1 as you have done?)

 

[mitchmcsscm94]

i did the KE+KE=KEf+KEf
I ended up with basically the same thing only the magnitude is squared. would the first ball come to rest and give ball 2 all its energy? that would mean that ball 2 would have a vfinal of 5.7 m/s. would that work? I am studying for a big test monday in AP Physics and this question has me beat.

 

[Nytik]

You missed my second point. Since the collision is in two dimensions, you have two equations for conservation of linear momentum- one in the x-direction, and one in the y-direction.
Of course KE is only concerned with the magnitude of the velocity, so there is no need to resolve your KE equation into components.