Question

Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in an elastic, glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed of 6.00 m/s. After the collision, the orange disk moves along a direction that makes an angle of 36.0° with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk.

orange disk ----------------m/s

yellow disk -----------------m/s

Answer 1

here,

the initial speed of orange disk , u = 6 m/s

theta = 36 degree

let the final speed of each disk be v1 and v2

using conservation of momentum

m * u i = m * v1 * ( cos(36) i + sin(36) j) + m * v2 * ( cos(90 - 36) i - sin(90 - 36) j)

6 i = v1 * ( 0.809 i + 0.588 j) + v2 * ( 0.588 i - 0.809 j)

on compairing the components

6 = 0.809 * v1 + 0.588 * v2 ....(1)

and

0 = 0.588 * v1 - 0.809 * v2 ......(2)

from (1) and (2)

v1 = 4.85 m/s

v2 = 3.53 m/s

the final speed of orange disk is 4.85 m/s

the final speed of yellow disk is 3.53 m/s