Final answer:
The impulse delivered to the ball by the racket is -5.4 kg·m/s, and the work done by the racket on the ball is -27 J. None of the answer choices provided in the question are correct.
Step-by-step explanation:
The impulse delivered to the ball by the racket can be calculated as follows:
- Impulse (J) = Change in momentum = final momentum - initial momentum.
- Initial momentum = mass × initial velocity = 0.06 kg × 50 m/s = 3 kg·m/s (positive since it's to the right).
- Final momentum = mass × final velocity = 0.06 kg × (-40 m/s) = -2.4 kg·m/s (negative since it's to the left).
- Change in momentum = -2.4 kg·m/s - 3 kg·m/s = -5.4 kg·m/s.
- Thus, the impulse delivered to the ball by the racket is -5.4 kg·m/s.
To calculate the work done by the racket on the ball:
- Work (W) = Change in kinetic energy = final kinetic energy - initial kinetic energy.
- Initial kinetic energy = 0.5 × mass × (initial velocity)^2 = 0.5 × 0.06 kg × (50 m/s)^2 = 75 J.
- Final kinetic energy = 0.5 × mass × (final velocity)^2 = 0.5 × 0.06 kg × (40 m/s)^2 = 48 J.
- Change in kinetic energy = 48 J - 75 J = -27 J.
- The work done by the racket on the ball is -27 J, which means the ball has lost 27 J of energy.
Since none of the provided answer choices match these calculations, the correct response is that none of the answer choices are correct.