Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. One is moving upward along the yaxis at 3.00 m/s, the other is moving to the right along the xaxis with speed 4.80 m/s. After the collision (assumed elastic), the second ball is moving along the positive yaxis. What is the final direction of the first ball and what are their two speeds after the collision.
Can someone please show me stepbystep how to solve this problem? Thank you!
1 Answer

let mass = 1 kg for simplicity
momentum of first is 3 kgm/s in y direction
momentum of second is 4.8 kgm/s in x direction.
After collision the total momentum has to match that before the collision in both x and y components.
total momentum is √(3² + 4.8²) = 5.66
Assume angle a for #1, angle with the +x axis
then total y component is V1sina + V2
and total x component is V1cosa
set them equal to initial x and y components
V1sina + V2 = 3
V1cosa = 4.8
total momentum is
√((V1sina+V2)² + (V1cosa)²) = 5.66
(V1sina+V2)² + (V1cosa)² = 32.04
V1²sin²a + V2² + 2V1V2sina + V1²cos²a = 32.04
V1²(sin²a+cos²a) + V2² + 2V1V2sina = 32.04
V1² + V2² + 2V1V2sina = 32.04
V1sina = 3 – V2
V1² + V2² + 2V2(3 – V2) = 32.04
V1² + V2² + 6V2 – 2V2² = 32.04
V1² – V2² + 6V2 = 32.04
3 equations 3 unknowns
V1² – V2² + 6V2 = 32.04
V1sina + V2 = 3
V1cosa = 4.8
intuitively I know that a is zero, let’s see if that is a solution.
plugging that in
V2 = 3
V1 = 4.8
does that solve the 3rd equation?
V1² – V2² + 6V2 = 32.04
23.04 – 9 + 18 = 32.04
yes.