Two shuffleboard disks of equal mass, one orange and the other yellow, are invol

Question

Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in a perfectly elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk, which is moving with a speed of 5.0 m/s. After the collision, the orange disk moves in a direction that makes an angle of 37° with its initial direction of motion, and the velocity of the yellow disk is perpendicular to that of the orange disk (After the collision, assume a negative 13° angle). Determine the final speed of each disk.

Explanation / Answer

mo = mass of orange disk = m = mass of yellow disk = my

Voo = initial velocity of orange = 5 m/s

Voy = initial velocity of yellow = 0 m/s

Using conservation of momentum along X-direction

m Voo + m Voy = m Vfo Cos37 + m Vfy Cos53

Vfo Cos37 + Vfy Cos53 = 5

Vfo = (5 - (Vfy Cos53)) / Cos37                              eq-1

using conservation of momentum along Y-direction

0 = m Vfo Sin37 - m Vfy Sin53

Using eq-1

(5 - (Vfy Cos53)) Sin37 / Cos37 = Vfy Sin53

Vfy = 3.01 m/s

Using eq-1

Vfo = (5 - (Vfy Cos53)) / Cos37 = (5 - ((3.01)Cos53)) / Cos37

Vfo = 3.99 m/s

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