A 10.0 g object moving to the right at 19.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 30.0 cm/s. Find the velocity of each object after the collision.

When the objects are moving in opposite directions

v₁= {-2m₂•v₂₀ +(m₁-m₂)•v₁₀}/(m₁+m₂)
v₂={ 2m₁•v₁₀ - (m₂-m₁)•v₂₀}/(m₁+m₂)

To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.

1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.

Momentum = mass * velocity

Let's assign positive velocities to objects moving to the right and negative velocities to objects moving to the left.

The initial momentum before the collision can be calculated as follows:

Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)

Given:
mass1 = 10.0 g = 0.01 kg (converting grams to kilograms)
velocity1 = 19.0 cm/s = 0.19 m/s (converting centimeters to meters, retaining the positive direction)
mass2 = 15.0 g = 0.015 kg (converting grams to kilograms)
velocity2 = -30.0 cm/s = -0.3 m/s (converting centimeters to meters, assigning opposite direction as negative)

Initial momentum = (0.01 kg * 0.19 m/s) + (0.015 kg * -0.3 m/s)

2. Conservation of kinetic energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Kinetic energy = (1/2) * mass * velocity^2

The initial kinetic energy before the collision can be calculated as follows:

Initial kinetic energy = (0.5 * mass1 * velocity1^2) + (0.5 * mass2 * velocity2^2)

Let's substitute the given values:

Initial kinetic energy = (0.5 * 0.01 kg * (0.19 m/s)^2) + (0.5 * 0.015 kg * (-0.3 m/s)^2)

Now we have two equations: one for conservation of momentum and one for conservation of kinetic energy. We can solve these equations to find the final velocities of the objects after the collision.

Let me do the calculations.