A 0.210 kg plastic ball moves with a velocity of 0.30 m/s. It collides with a second plastic ball of mass 0.109 kg, which is moving along the same line at a speed of 0.10 m/s. After the collision, both balls continue moving in the same, original direction, and the speed of the 0.109 kg ball is 0.26 m/s. What is the new velocity of the first ball?

Whatever conserves momentum.

Initial total momentum = Final total momentum

You have to do the calculation along one axis only in this case, since they remain traveling in the same direction.

To find the new velocity of the first ball after the collision, we can apply the principles of conservation of momentum.

The principle of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision, provided no external forces act on the system.

The momentum of an object is defined as its mass multiplied by its velocity. Mathematically, it can be stated as:

Momentum = mass × velocity

In this case, the momentum of the system before the collision is equal to the momentum of the system after the collision. Therefore, we can express this as:

(mass of the first ball × velocity of the first ball)before + (mass of the second ball × velocity of the second ball)before = (mass of the first ball × velocity of the first ball)after + (mass of the second ball × velocity of the second ball)after

Let's substitute the known values:

(0.210 kg × 0.30 m/s) + (0.109 kg × 0.10 m/s) = (0.210 kg × new velocity of the first ball) + (0.109 kg × 0.26 m/s)

Simplifying the equation:

0.063 kg·m/s + 0.0109 kg·m/s = 0.210 kg · new velocity of the first ball + 0.02834 kg·m/s

Combining like terms:

0.0739 kg·m/s = 0.210 kg · new velocity of the first ball + 0.02834 kg·m/s

Now, subtracting 0.02834 kg·m/s from both sides:

0.0739 kg·m/s - 0.02834 kg·m/s = 0.210 kg · new velocity of the first ball

0.04556 kg·m/s = 0.210 kg · new velocity of the first ball

To find the new velocity of the first ball, we need to divide both sides of the equation by 0.210 kg:

(0.04556 kg·m/s) / 0.210 kg = new velocity of the first ball

Calculating:

new velocity of the first ball ≈ 0.217 m/s

Therefore, the new velocity of the first ball after the collision is approximately 0.217 m/s.