1) 

Three spheres of equal mass, 0.99 kg and radius 0.117 m are arranged to collide elastically as shown below.

The blue sphere comes in from the right at velocity 1 m/s and collides simultaneously with the two red spheres.  Due to symmetry, the red spheres leave with velocities of equal magnitude, v, and at equal angles, theta, above and below the horizontal axis, respectively.  The blue sphere has a final velocity, v' with no y-component (again due to symmetry) after the collision.  Determine the final velocity (in m/s), with the sign indicating the direction of the velocity in the x direction, of the blue sphere after the collision.

2)

Three spheres of equal mass, 1.36 kg and radius 0.295 m are arranged to collide as shown below.

The blue sphere comes in from the right at a velocity of 1.2 m/s and collides simultaneously with the two red spheres.  Due to symmetry, the red spheres leave with velocities of equal magnitude, v, and at equal angles, theta, above and below the horizontal axis, respectively.  The blue sphere has a velocity, I'm with no y-component (again due to symmetry) after the collision.  This time there is energy, 0.5 J, lost in the collision. Determine the final speed shared by each of the red spheres (in m/s) after the collision.

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