A 10 kg ball moving due west at 2m/sec collided with a 4kg ball that is moving due east at 3m/sec. you determine that immediately after the collision the 10 kg ball is moving due west at .57 m/sec.

a) this probably is a totally elastic collision
b) this definitely is NOT a totally inelastic collision
c) more info is needed

we are to show all of our work.

To determine whether the collision is totally elastic, totally inelastic, or if more information is needed, we can use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of a system before a collision is equal to the total momentum after the collision, assuming there are no external forces acting on the system.

Let's start by calculating the initial momentum of the system before the collision. Momentum is calculated by multiplying mass and velocity.

The initial momentum of the 10 kg ball, moving due west at 2 m/s, can be calculated as:
Momentum1 = mass1 * velocity1
Momentum1 = 10 kg * (-2 m/s) [taking east as positive and west as negative]
Momentum1 = -20 kg*m/s

The initial momentum of the 4 kg ball, moving due east at 3 m/s, can be calculated as:
Momentum2 = mass2 * velocity2
Momentum2 = 4 kg * 3 m/s
Momentum2 = 12 kg*m/s

The total initial momentum of the system is the sum of the individual momenta:
Total initial momentum = Momentum1 + Momentum2
Total initial momentum = (-20 kg*m/s) + (12 kg*m/s)
Total initial momentum = -8 kg*m/s

Now, let's determine the final momentum of the system after the collision, using the given information that the 10 kg ball is moving due west at 0.57 m/s.

The final momentum of the 10 kg ball can be calculated as:
Final momentum1 = mass1 * velocity1
Final momentum1 = 10 kg * (-0.57 m/s) [taking east as positive and west as negative]
Final momentum1 = -5.7 kg*m/s

The final momentum of the 4 kg ball remains the same as its initial momentum, as no information is provided about its final velocity.

Now, let's calculate the total final momentum of the system:
Total final momentum = Final momentum1 + Momentum2
Total final momentum = (-5.7 kg*m/s) + (12 kg*m/s)
Total final momentum = 6.3 kg*m/s

Since the total initial momentum of the system is -8 kg*m/s and the total final momentum is 6.3 kg*m/s, we can see that the total momentum is conserved. Therefore, the collision is a totally elastic collision (option a) is correct).

To determine whether the collision is totally inelastic or if more information is needed, we would need to calculate the final velocity of the 4 kg ball. However, we don't have this information. Therefore, we cannot conclusively say that the collision is totally inelastic (option b) is incorrect), and we also cannot determine if more information is needed (option c) is incorrect).