please help.. i really need the answer as soon as possible..

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 moving initially to the right at 7.00 ms"1. After the collision, the orange disk
moves in a direction that makes an angle of 39°.with its initial direction. Meanwhile, the
velocity vector of the yellow disk is perpendicular to the post collision velocity vector of the
orange disk.

a) Determine the speed of each disk after the collision.

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To determine the speed of each disk after the collision, we need to apply the principles of conservation of momentum and conservation of kinetic energy.

1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision. Since the yellow disk is initially at rest, its momentum is zero. The momentum of the orange disk before the collision can be calculated as the product of its mass and initial velocity: momentum = mass × velocity.

2. Conservation of kinetic energy:
Since the collision is perfectly elastic, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. The kinetic energy of an object is given by the formula: kinetic energy = 0.5 × mass × velocity^2.

Now, let's go step by step to calculate the speed of each disk after the collision:

Step 1: Determine the momentum and kinetic energy before the collision:
- Momentum of the orange disk before the collision = mass × velocity = mass × 7.00 m/s.
- Total momentum before the collision = momentum of the orange disk before the collision.
- Kinetic energy before the collision = 0.5 × mass × velocity^2 = 0.5 × mass × (7.00 m/s)^2.

Step 2: Determine the momentum and kinetic energy after the collision:
- Calculate the resulting velocity of the orange disk after the collision by resolving its velocity vector into horizontal and vertical components using the given angle.
- Momentum of the orange disk after the collision = mass × velocity of the orange disk after the collision.
- Calculate the velocity of the yellow disk after the collision based on the information given.

Step 3: Apply the conservation principles:
- Equate the total momentum before the collision to the total momentum after the collision.
- Equate the total kinetic energy before the collision to the total kinetic energy after the collision.

Step 4: Solve the equations simultaneously to find the speeds of each disk after the collision.

Note: Since you provided the masses of the disks, I assume that the mass values are known. If not, those values would be needed to determine the speeds of each disk after the collision.