A baseball has a mass of 155 g, and a top major league pitcher can throw it at 50.5 m/s. If an 75.5 kg pitcher was standing on a sheet of ice and then threw the ball, what would his recoil speed be? 9.65 cm/s 10.4 cm/s 24.6 cm/s 104 cm/s

This problem can be solved using the principle of conservation of momentum. The total momentum before the throw is equal to the total momentum after the throw.

The momentum of the system before the throw is 0 because neither the pitcher nor the ball is moving. After the throw, the ball has momentum and the pitcher has recoil momentum.

The momentum of the ball is its mass times its velocity, and the momentum of the pitcher is his mass times his recoil velocity.

So, we can set up the equation as follows:

0 = momentum of the ball + momentum of the pitcher 0 = (mass of the ball * velocity of the ball) + (mass of the pitcher * recoil velocity of the pitcher)

We can rearrange the equation to solve for the recoil velocity of the pitcher:

recoil velocity of the pitcher = - (mass of the ball * velocity of the ball) / mass of the pitcher

Substituting the given values:

recoil velocity of the pitcher = - (0.155 kg * 50.5 m/s) / 75.5 kg

Solving this equation gives the recoil velocity of the pitcher. The negative sign indicates that the direction of the pitcher's recoil is opposite to the direction of the ball's motion.

Let's calculate it.

recoil velocity of the pitcher = - (0.155 kg * 50.5 m/s) / 75.5 kg = -0.104 m/s

Converting this to cm/s (since the options are given in cm/s), we get:

recoil velocity of the pitcher = -0.104 m/s * 100 = -10.4 cm/s

So, the recoil speed of the pitcher would be 10.4 cm/s. The negative sign just indicates the direction is opposite to the throw, but speed is a scalar quantity, so we take the absolute value. Therefore, the answer is 10.4 cm/s.