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 v with arrowoi = 3.10 m/s as in Figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of = 40.0° with the horizontal axis while the green disk makes an angle of phi = 50.0° with this axis as in figure (b). Determine the speed of each disk after the collision.

Explanation / Answer

Let M be mass of each disk,
Initial momentum = 3.1 * M i
FInal momentum = ((Vof * M * cos theta) + (Vgf * M * cos phi)) i + ((Vof * M * sin theta)-(Vgf * M * sin phi)) j
FInal momentum = ((Vof * M * 0.766 ) + (Vgf * M * 0.6428)) i + ((Vof * M * 0.6428)-(Vgf * M * 0.766)) j
So by conservation of momentum
Initial momentum = FInal momentum
3.1 * M i = ((Vof * M * 0.766 ) + (Vgf * M * 0.6428)) i + ((Vof * M * 0.6428)-(Vgf * M * 0.766)) j
3.1 = (Vof * 0.766 ) + (Vgf * 0.6428)
0 = (Vof * 0.6428)-(Vgf * 0.766)
Vof = 1.19173 * Vgf
so , 3.1 = (1.19173 * Vgf *0.766) + (Vgf * 0.6428)
Vgf = 1.9927 m/s
Vof = 2.3748 m/s

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