Elastic collision shuffleboard problem

[KD-jay]

Homework Statement

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 5.40 m/s. After the collision, the orange disk moves along a direction that makes an angle of 40.0° with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. Determine the final speed of each disk.

Homework Equations

p_i = p_f
KE_i=KE_f

The Attempt at a Solution

X-Direction

Orange Shuffleboard
Initial Momentum = 5.4m
Final Momentum = V_ofcos(40)m
Initial KE = (1/2)(m)(5.4)²
Final KE = (1/2)(m)(V_of)²

Yellow Shuffleboard
Initial Momentum = 0
Final Momentum = V_yfcos(90-40)m
Initial KE = 0
Final KE = (1/2)(m)(V_yf)²

Conservation of Momentum
5.4m + 0 = V_ofcos(40)m + V_yfcos(50)m

Conservation of Energy
(1/2)(m)(5.4)² + 0 = (1/2)(m)(V_of)² + (1/2)(m)(V_yf)²

Y-Direction

Orange Shuffleboard
Initial Momentum = 0
Final Momentum = V_ofsin(40)m
Initial KE = (1/2)(m)(5.4)²
Final KE = (1/2)(m)(V_of)²

Yellow Shuffleboard
Initial Momentum = 0
Final Momentum = V_yfsin(50)m
Initial KE = 0
Final KE = (1/2)(m)(V_fy)²

Conservation of Momentum
0 + 0 = V_ofsin(40)m + V_yfsin(50)m

Conservation of Energy
(1/2)(m)(5.4)² + 0 = (1/2)(m)(V_of)² + (1/2)(m)(V_fy)²

I know I'm supposed to use all these equations to solve for the unknowns but I just want to make sure I'm on the right track. Are all my variables correct? Also, it seems extremely tedious to solve this system of equations, would it be safe to just cross out the masses on the momentum conservation and the (1/2)m on the energy conservations? Thanks.

 

[LowlyPion]

The masses are all equal so no need to account for that.

Basically it looks like you have the right method. Careful of your signs in solving

 

[Marthius]

never mind, I misread the problem (deleted now)