The equation for momentum is given as:

Where  is the momentum of an object,  is the mass of the object, and  is the velocity of the object.

For Ball 1 we have:

For Ball 2 we have:

So the balls have equivalent momentum.

The equation for momentum is given as:

Where  is the momentum of an object,  is the mass of the object, and  is the velocity of the object.

The relationship between momentum and velocity is linear, so when the objects velocity is doubled, its momentum is also doubled.

We can use the expression for impulse for this problem:

Since we are given the mass and can easily calculate the change in velocity, we'll go with the second form of this expression:

Conservation of momentum states that the angular momentum of the golf swing transfers into the linear momentum of the golf ball, or . Since the only forces acting on the ball are kinetic friction and gravity, we can use kinematics to put this equation completely into known quantities.

Solving for  gives . Kinematics gives that . Substituting the first expression into the second gives that .

The kinetic friction force can be expressed as  and by Newton's second law, . Hence the acceleration due to friction can be written as . Substituting this into our previous kinematic expression finally gives

. Plugging in known values gives . Solving for  gives 

Using the equation for momentum,

If the mass stays constant and the velocity doubles, the momentum must double as well to balance the equation.

Because we are solving for two velocities (two unknowns), we need two equations. We can use the conservation of linear momentum:

Because we know that the collision is elastic, we know that kinetic energy is conserved:

The red ball starts at rest so

The above equations can then be simplified and one can solve for and .

Negative implies the ball is moving to the left.

Using conservation of momentum

Solving for 

Plugging in values:

(A negative value is assumed for Tommy's direction for simplicity, a negative could have been used for Jennifer's instead, it will yield the same result.

A coordinate system isn't immediately given, so the first step is to establish an x- and y-direction. Let the first ship travel in the positive y-direction with the second traveling  from the y-axis.

The linear momentum for the first ship is given by 

and for the second ship by 

Conservation of linear momentum says that . Thus the final velocity can be expressed as

Further,

The final speed is then 

This question tests your understanding of the concept of conservation of momentum. More specifically, this tests your understanding of perfectly inelastic collisions, or collisions in which the two colliding particles stick together and move together as a system. 

By conservation of momentum, the initial total momentum of a system is equal to the final total momentum of the system. The formula for the momentum of an object is equal to the mass of the object multiplied by the velocity of the object. When applying the conservation of momentum formula to perfectly inelastic collisions, you consider the two objects as a single mass after they collide, since they stick together and travel together. Thus, this problem can be solved as follows:

The final velocity of the  ball unit is therefore (sign is positive because initially the  ball was traveling to the right, and its velocity was positive, and when the  ball unit formed and moved, it continued moving in the rightward, positive direction.

This question tests your understanding of the conservation of momentum, which states that momentum (mass multiplied by velocity) can neither be created nor destroyed in a system. In this elastic collision, we are presented with two blocks (one initially moving, and one initially stationary), that collide such that each block is moving separately afterwards and neither loses energy to friction or other forces. You can set up the equation as follows:

Therefore, the final velocity of the  block is  in the positive direction.