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# Answer to Question #106029 in Mechanics | Relativity for Valentine Agun

Question #106029
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 5.00 m/s as in Figure P6.40a. After the collision, the orange disk moves in a direction that makes an angle of 37.0° with the horizontal axis while the green disk makes an angle of 53.0° with this axis as in Figure P6.40b. Determine the speed of each disk after the collision.
1
2020-03-23T12:21:46-0400

It is case of elastic collision.

We have to apply the momentum conservation equation for both horizontal a d vertical direction.

"(sin \\ 37 \\degree=cos\\ 53\\degree=\\frac{3}{5};sin\\ 53\\degree=cos \\ 37\\degree=\\frac{4}{5})"

Let the velocity of green ball be "v_g" and that of orange is "v_o."

Applying momentum conservation in horizontal axis,

"5=v_o cos\\ 37\\degree+v_gcos \\ 53\\degree"

"\\implies 4v_o+3v_g=25\\ \\ \\ (1)"

Applying momentum conservation in vertical direction,

"0=v_osin\\ 37\\degree-v_gsin \\ 53\\degree"

"\\implies v_o=\\frac{4}{3}v_g"

Substituting this in "(1),"

"4\\times \\frac{4}{3}v_g+3v_g=25"

"\\implies v_g=3\\ m\/sec"

"\\implies v_o=\\frac{4}{3}v_g=\\frac{4}{3}\\times 3=4\\ m\/sec"

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