Two shuffleboard disks of equal mass, one orange and the other green, are involv

Question

Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at vOi = 4.95 m/s as in Figure a, shown below. After the collision, the orange disk moves in a direction that makes an angle of = 36.0° with the horizontal axis while the green disk makes an angle of = 54.0° with this axis as in Figure b. Determine the speed of each disk after the collision.

vof = ___ m/s

vgf = ___ m/s

Explanation / Answer

The sum of their vertical momenta is zero:
1) Vo*sin36° = Vg*sin54°

The sum of their horizontal momenta must equal the initial momentum of orange:
2) Vo*cos36° + Vg*cos54° = 4.95

In each case, since the masses are equal, they cancel out.

Solving (1) & (2) simultaneously,
Vo = 4.877 m/s
Vg = 3.543 m/s

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