Question

g during a tennis serve, the ball is tossed vertically in the air with a speed of 1.2 m/s. when the ball reaches apex of it's flight, the tennis player hits the ball with their 306 g tennis racket. just before collision, the racket is moving at a velocity of 43.1 m/s. post-collision, the ball is moving at a velocity of 51.0 m/s. if during the collision, the ball and racket had a coefficient of restitution of 0.737, what is the post-collision velocity (m/s) of the racket?

Answer 1

To find the post-collision velocity of the racket, use the law of conservation of momentum and solve the equation.

Step-by-step explanation:

The post-collision velocity of the racket can be calculated using the law of conservation of momentum.

Let's say the mass of the racket is m.

Before the collision, the ball is moving at a velocity of 51.0 m/s and has a mass of 0.306 kg. After the collision, the ball and the racket move together with a velocity of 43.1 m/s.

Using the law of conservation of momentum, we can write:
Mass of ball x velocity of ball + mass of racket x velocity of racket = (mass of ball + mass of racket) x velocity of racket after collision

Plugging in the values:
0.306 kg x 51.0 m/s + m x 43.1 m/s = (0.306 kg + m) x 43.1 m/s x 0.737

By solving this equation, we can find the value of m which represents the post-collision velocity of the racket.

Answer 2

The post-collision velocity of the racket is approximately -24.46 m/s.

Step-by-step explanation:

The post-collision velocity of the racket can be found using the equation for the coefficient of restitution.

The coefficient of restitution is defined as the ratio of the final relative velocity of two objects after a collision to their initial relative velocity:e = (v_f2 - v_f1) / (v_i2 - v_i1)

where e is the coefficient of restitution, v_f1 and v_f2 are the final velocities of the ball and racket respectively, and v_i1 and v_i2 are their initial velocities.

Using the given values, we can rearrange the equation to solve for the post-collision velocity of the racket: 51.0 m/s - 1.2 m/s = 0.737(43.1 m/s - v_i1)

Solving for v_i1: v_i1 = 43.1 m/s - (51.0 m/s - 1.2 m/s) / 0.737

= 43.1 m/s - 49.8 m/s / 0.737

= 43.1 m/s - 67.56 m/s

= -24.46 m/s

Therefore, the post-collision velocity of the racket is approximately -24.46 m/s.