Final answer:
To find the velocity of the target ball after an elastic collision and the mass of the target ball, conservation of momentum and kinetic energy must be applied. Without additional information or numerical values for the final velocity, we cannot provide an exact answer as the calculation requires specific data on the velocity after the collision.
Step-by-step explanation:
To calculate the velocity of the target ball after the collision and the mass of the target ball when a 0.220 kg ball collides elastically and the incoming ball bounces backward, we must apply the conservation of momentum and the conservation of kinetic energy which are both principles in elastic collision scenarios. We have the following data:
- Mass of ball 1 (m1) = 0.220 kg
- Initial velocity of ball 1 (u1) = 7.5 m/s
- Final velocity of ball 1 (v1) = -3.8 m/s (negative because it's moving in the opposite direction after collision)
- Mass of ball 2 (m2) = unknown
- Initial velocity of ball 2 (u2) = 0 m/s (at rest)
- Final velocity of ball 2 (v2) = unknown
To solve for v2, we apply the conservation of momentum:
Initial momentum = Final momentum
m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2
For part (b), we need to use the conservation of kinetic energy since the collision is elastic:
Initial kinetic energy = Final kinetic energy
½ * m1 * u1^2 + ½ * m2 * u2^2 = ½ * m1 * v1^2 + ½ * m2 * v2^2
Using these equations, we can solve for v2 and m2. However, since we need a specific answer and no numerical value is provided for the velocity of the target ball, we can't calculate the exact numbers without additional data assuming a perfectly elastic collision.