Two snowballs with masses of 0.48 kg and 0.81 kg, respectively, collide head-on and combine to form a single snowball. The initial speed for each is 14 m/s. If the velocity of the new combined snowball is 2.4 m/s after the collision, what is the decrease in kinetic energy?

If the problem asks for the change in the kinetic energy after the collision took place then the difference between the final and initial total kinetic energy must be determined!

Finding the value of the initial kinetic energy (Ki)

Before the collision, the two snowballs move toward each other, this indicates that [tex]\rm K_i[/tex] is the sum of two snowballs' individual kinetic energies.

Both snowballs move at the same speed but, in different directions (one is going to the left while the other is going right), thus one of the them will have a +14 m/s and the other will have -14 m/s.

Regardless, it doesn't matter which has the positive or negative value since the velocity part of kinetic energy is squared.

So,

[tex]K_i=\frac{1}{2} mv^2+\frac{1}{2} mv^2\\\\=\frac{1}{2} (0.48)(14)^2+\frac{1}{2} (0.81)(-14)^2\\\\=47.04+79.38\\\implies126J[/tex]

Find the value of the final kinetic energy (Kf)

After the collision, the two snowballs join together, having the same mass, and move in the same direction (positive or negative, again it doesn't matter) at the same speed of 2.4 m/s. This means that we're finding the kinetic energy of a single snowball, consisting of the two snowballs' mass.

So,

[tex]K_f=\frac{1}{2} mv^2\\\\=\frac{1}{2} (0.48+0.81)(2.4)^2\\\\\implies4J[/tex]

The final step

All there's left is to take the difference between Kf and Ki.

[tex]4J-126J=-122J[/tex]