Question

A tennis player swings her 1000 g racket with a speed of 15.0 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 18.0 m/s. The ball rebounds at 40.0 m/s.

How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.
_________m/s

Answer 1

The racket is moving at a velocity of 121.2 m/s immediately after the impact.

Step-by-step explanation:

To find out how fast the racket is moving immediately after the impact, we can use the law of conservation of momentum. The momentum of an object is given by the product of its mass and velocity. Before the impact, the momentum of the racket is 1000 g * 15.0 m/s = 15000 g·m/s. The momentum of the ball is 60 g * 18.0 m/s = 1080 g·m/s. After the impact, the ball rebounds with a speed of 40.0 m/s. To find the velocity of the racket, we can use the conservation of momentum equation: (racket momentum before impact) + (ball momentum before impact) = (racket momentum after impact) + (ball momentum after impact)

15000 g·m/s + 1080 g·m/s = (racket mass)(racket velocity after impact) + (60 g)(40.0 m/s)

Converting the masses to kg and solving for the racket velocity after impact:

15 kg·m/s = (racket mass)(racket velocity after impact) + 2.88 kg·m/s

(racket mass)(racket velocity after impact) = 15 kg·m/s - 2.88 kg·m/s

(racket mass)(racket velocity after impact) = 12.12 kg·m/s

Dividing both sides by the racket mass:

racket velocity after impact = 12.12 kg·m/s / 0.1 kg

racket velocity after impact = 121.2 m/s