Two balls collide on a horizontal, frictionless table. Ball A has a mass of 0.175 kg and travelling at 1.20 m/s [E 40o S]. Ball B has a mass of 0.225 kg and is travelling at 0.68 m/s [E]. The velocity of ball B after collision is 0.93 m/s [E 23o S]. What is the velocity of ball A after the collision? What percentage of the kinetic energy is lost in the collision?

Break the problem into E-W components, and N-S components.

Then solve by use of conservation of momentum in each of those directions.

To find the velocity of ball A after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Let's assume the initial velocity of ball A is vAi, and the velocity of ball B is vBi. The direction angles are given as well.

Before collision:
The momentum of ball A before the collision is given by:
MomentumA_initial = massA × velocityA_initial
= 0.175 kg × 1.20 m/s [E 40° S]

Now, since we are given the velocity of ball B after the collision, we need to break it down into its x and y components. Using trigonometry, we can calculate the x-component velocity (vBxf) and y-component velocity (vByf):
vBxf = velocityB_final × cos(angle)
= 0.93 m/s × cos(23°) [E]

vByf = velocityB_final × sin(angle)
= 0.93 m/s × sin(23°) [S]

Next, we can find the individual momentum components:
MomentumB_initial_x = massB × velocityB_initial_x
= 0.225 kg × 0.68 m/s [E]

MomentumB_initial_y = massB × velocityB_initial_y
= 0.225 kg × 0 m/s [S] (since ball B is traveling only horizontally)

Since the collision is happening on a horizontal frictionless table, the total momentum in the y-direction remains constant. Therefore, MomentumB_initial_y = MomentumB_final_y.

Finally, we can write the conservation of momentum equation:
MomentumA_initial + MomentumB_initial_x = MomentumA_final + MomentumB_final_x

Substituting the given values into the equation and solving for MomentumA_final will give us the velocity of ball A after the collision.

To calculate the percentage of kinetic energy lost in the collision, we can use the following formula:

Percentage of kinetic energy lost = (Initial kinetic energy - Final kinetic energy) ÷ Initial kinetic energy × 100

The initial kinetic energy is given by:
Initial kinetic energy = 0.5 × massA × velocityA_initial^2 + 0.5 × massB × velocityB_initial^2

The final kinetic energy is given by:
Final kinetic energy = 0.5 × massA × velocityA_final^2 + 0.5 × massB × velocityB_final^2

Substituting the values and solving for the percentage of kinetic energy lost will give us the desired result.