Packages in an automobile parts supply house are transported to the loading dock by pushingthem along on a roller track with very little friction. At the instant shown packages B and Care at rest and package A has a velocity of 2 m/s. Knowing the coefficient of restitutionbetween the packages is 0.3, determinea) the velocity of package C after A hits B and B hits C

To solve this problem, we need to use the principle of conservation of momentum and the coefficient of restitution.

Step 1: Conservation of Momentum The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

Step 2: Coefficient of Restitution The coefficient of restitution is a value that represents the ratio of speeds after and before an impact, taken along the line of the impact.

Given: Mass of A, B, C are m1, m2, m3 respectively. Initial velocity of A is u1 = 2 m/s, B and C are at rest, so u2 = u3 = 0. Coefficient of restitution e = 0.3.

When A hits B: Using the principle of conservation of momentum, m1u1 = m1v1 + m2*v2. Using the coefficient of restitution, e = (v2 - v1) / u1. Solving these two equations, we can find the velocities v1 and v2 after A hits B.

When B hits C: Again, using the principle of conservation of momentum, m2v2 = m2v2' + m3*v3. Using the coefficient of restitution, e = (v3 - v2') / v2. Solving these two equations, we can find the velocities v2' and v3 after B hits C.

The velocity of package C after A hits B and B hits C is v3.

Note: This solution assumes that the masses of the packages are known. If the masses are not given, we cannot solve this problem as it is currently stated.