A baseball has a mass of 155 g, and a top major league pitcher can throw it at 54.0 m/s. If an 81.0 kg pitcher was standing on a sheet of ice and then threw the ball, what would his recoil speed be? 10.3 cm/s 103 cm/s 28.2 cm/s 9.68 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.

The momentum of the system after the throw is the sum of the momentum of the ball and the momentum of the pitcher.

Momentum is calculated as the product of mass and velocity.

The momentum of the ball after the throw is its mass times its velocity, which is 155 g * 54.0 m/s. However, we need to convert the mass from grams to kilograms because the standard unit of mass in physics is the kilogram. So, the mass of the ball is 155 g = 0.155 kg.

Therefore, the momentum of the ball is 0.155 kg * 54.0 m/s = 8.37 kg*m/s.

Since the total momentum before the throw was 0, the total momentum after the throw must also be 0. This means that the momentum of the pitcher must be -8.37 kg*m/s (the negative sign indicates that the direction of the pitcher's momentum is opposite to that of the ball's momentum).

The mass of the pitcher is given as 81.0 kg. We can find his velocity by dividing his momentum by his mass.

So, the velocity of the pitcher is -8.37 kg*m/s / 81.0 kg = -0.103 m/s.

The negative sign indicates that the direction of the pitcher's velocity is opposite to that of the ball's velocity. In terms of magnitude, the pitcher's recoil speed is 0.103 m/s.

To convert this to cm/s, we multiply by 100 (since 1 m = 100 cm).

So, the pitcher's recoil speed is 0.103 m/s * 100 = 10.3 cm/s.

Therefore, the correct answer is 10.3 cm/s.