Question

Two identical pucks are set on a collision course on an air table. After the collision, puck A has a final velocity of 5.00cm/s at an angle of 28 degrees from the vertical and puck B has a final velocity of 4.00cm/s at an angle of 32 degrees from the vertical. Determine the initial speeds of both pucks.

Answer 1

vertical ? I thought table was level. I will assume you mean from the y axis.

final momentum y component = m (5) cos 28 + m (4) cos 32
= 7.81 m

final momentum x component (I will assume one + and the other -)
= m (5) sin 28 - m(4) sin 32
= 2.18 m

Now I will have to assume something about the elasticity of the collision, like maybe perfectly elastic so energy is conserved
final Ke = (1/2)m (5^2 +4^2) = 20.5 m Joules

so
initial velocities
Ax i + Ay j
Bx i + By j

Ax + Bx = 2.18
Ay + By = 7.81

(1/2)(Ax^2+Ay^2) + (1/2)(Bx^2+By^2) = 20.5
or
Ax^2+ Ay^2 + Bx^2 + By^2 = 41
Solution:
They simply change x axis velocities (perfect bounce)
same speeds as in the beginning but opposite signs of x axis velocities and the same y axis velociies