This is an example of an inelastic collision, as the two cars stick together after colliding. We can assume momentum is conserved.

To make the equation easier, let's call the first car "1" and the second car "2."

Using conservation of momentum and the equation for momentum, , we can set up the following equation.

Since the cars stick together, they will have the same final velocity. We know the second car starts at rest, and the velocity of the first car is given. Plug in these values and solve for the final velocity.

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy. 

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for .

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy. 

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for .

This is an example of an elastic collision. We start with two masses and end with two masses with no loss of energy. 

We can use the law of conservation of momentum to equate the initial and final terms.

Plug in the given values and solve for .

The difference between an elastic and an inelastic collision is the loss or conservation of kinetic energy. In an inelastic collision kinetic energy is not conserved, and will change forms into sound, heat, radiation, or some other form. In an elastic collision kinetic energy is conserved and does not change forms.

Remember, total energy and total momentum are conserved regardless of the type of collision; however, while energy cannot be created nor destroyed, it can change forms.

In the answer options, only one choice preserves the total kinetic energy. The resulting bang from the car crash, the flame from the match, the sound of hands clapping, and the gamma radiation during hydrogen fusion are all examples of the conversion of kinetic energy to other forms, making each of these an inelastic collision. Only the neutron fusion described maintains the conservation of kinetic energy, making this an elastic collision.

Elastic collisions occur when two objects collide and kinetic energy isn't lost. The objects rebound from each other and kinetic energy and momentum are conserved. Inelastic collisions are said to occur when the two objects remain together after the collision so we are dealing with an elastic collision.

Above, the subscripts 1 and 2 denote puck A and B respectively, and the initial momentum of puck B is zero, so that term is not included in the equation above.

Plug in initial and final velocities and mass:

This is an inelastic collision as the two objects stick together and move together with the same velocity. Inelastic collisions conserve momentum, but they do not conserve kinetic energy.

We will need to start at the end of the situation and work backward in order to determine the velocity of the bullet.  At the very end, the pendulum with the bullet reaches its maximum height and therefore comes to a stop.  It has gravitational potential energy.  At the bottom of the pendulum right after the bullet collides with it, it has kinetic energy due to the velocity of the bullet.  With the law of conservation of energy, we can set the kinetic energy of the pendulum right after the collision equal to the gravitational potential energy of the pendulum at the highest point.

To determine the height of the pendulum we will need to use trig and triangles to find the height.  We know that the pendulum makes a 30-degree angle with the equilibrium position at its maximum height.  The length of the pendulum is provided which is the hypotenuse of this triangle.  We need to find the adjacent side of this triangle.  We can use cosine to determine this.

We can now subtract this value from the length of the pendulum to determine how high off the ground the pendulum is at its highest point. 

We can now set the kinetic energy of the pendulum right after the collision equal to the gravitational potential energy of the pendulum at the highest point.

The mass is the same throughout so it falls out of the equation.

The pendulum with the bullet was moving  after the collision.  We can now use momentum to determine the speed of the bullet before the collision.  Conservation of momentum states that the momentum before the collision must equal the momentum after the collision.

They both move together after the collision

Since the pendulum was not moving at the beginning

We can now plug in these values and solve for the missing piece.