In a collision, a 60 g marble rolling at 8.00 cm/s hits a stationary marble and moves off at 4.89 cm/s at a 27° angle. What is the mass of the second marble if it moves at 3.21 cm/s at 31.7°?

To determine the mass of the second marble in a collision scenario, we apply the principles of conservation of momentum. This principle states that in the absence of external forces, the total momentum before the collision must equal the total momentum after the collision.

First, we need to calculate the momentum of the first marble before the collision. The momentum is given by the product of mass and velocity. Since the first marble is moving at 8.00 cm/s, we convert the mass into kilograms (0.060 kg) and find the initial momentum of the first marble.

Next, we break down the momentum of both marbles into their x (horizontal) and y (vertical) components. The first marble's momentum components after the collision, moving at 4.89 cm/s and at an angle of 27°, can be calculated using trigonometric functions (cosine for the x-component and sine for the y-component).

For the second marble, which is moving at 3.21 cm/s at an angle of 31.7°, we will similarly calculate its momentum components.

After calculating the respective momentum components of both marbles post-collision, we set up equations based on the conservation of momentum for both the x and y components. This results