Relevant equations:

Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.

To calculate the impulse, know that it is equal to the change in momentum.

Write the impulse equation in terms of mass and velocity.

In our case, the initial velocity of the baseball is  and its final velocity is , where the negative sign indicates that the ball is traveling in the opposite direction. Also, m = 0.15kg. The impulse on the ball can be calculated below.

The negative sign tells that the force on the baseball is opposed to the original momentum.

We need to use conservation of momentum to solve this problem.

Initially, the pickup truck moves at . The load moves together with the truck so the load is also moving at .

We can calculate the truck-load momentum as follows:

Note that this is the sum of the truck's momentum AND the load's momentum. We are looking at is as a whole since they are moving together.

The car moves at . Be careful with signs here! The problem says it moves in the opposite direction. We used a positive velocity for the truck/load, so the velocity of the car should be negative if it is moving in the opposite direction. We can also see from the diagram that the car is moving to the left.

Therefore, we have that the momentum for the car as:

We can find the initial momentum of the system (truck, load, and car) via simple addition:

After the collision, we know that all three objects move together, so they all move with the same velocity. Therefore we can express the momentum of the system after the collision as follows:

 is the velocity of the objects after the collision. This is the sum of the momentum of all three objects; we were able to simplify the equation because they all move with the same velocity.

By conservation of momentum we know that the momentum of the system before the collision is equal to the momentum of the system after the collision.

Use this to solve for the final velocity.

Assuming the atoms have the same mass, a collision between atoms in a vacuum is most nearly an elastic collision. This means the kinetic energy of the system is conserved and when they collide, all of the kinetic energy in atom A will be transferred perfectly to atom B. So just after collision, atom A will have velocity  and atom B will have velocity . Note that momentum is always conserved.

The equation for conservation of momentum is:

Given:

Plug in given values into the conservation of momentum equation.

Simplify.

Subtract the final velocity from the initial velocity to find change in speed (since these velocities are in the same direction).

 .

Because of conservation of momentum, the product of the initial mass and velocity should equal the final mass and velocity. The equation for conservation of momentum is:

The initial mass of the truck is 

The initial velocty is 

The final velocity is  

Plug in known values to the conservation of momentum equation.

Simplify.

Note that while necessary, the final mass is not our final answer. The final mass, , is the mass of the truck, , and the mass of the sand added to the truck, .

The mass of the truck is known so set up an equation and solve for the mass of sand added to the truck.