A baseball has a mass of 145 g, and a top major league pitcher can throw it at 41.5 m/s. If an 86.0 kg pitcher was standing on a sheet of ice and then threw the ball, what would his recoil speed be?

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.

Step 1: Convert the mass of the baseball into kg, because the mass of the pitcher is given in kg. 1 g = 0.001 kg, so 145 g = 0.145 kg.

Step 2: Calculate the momentum of the baseball after the throw. Momentum (p) is calculated as the product of mass (m) and velocity (v). So, p = m * v. For the baseball, p = 0.145 kg * 41.5 m/s = 6.0125 kg*m/s.

Step 3: Since the total momentum before the throw was zero (as both the pitcher and the baseball were initially at rest), the total momentum after the throw must also be zero. This means the momentum of the pitcher must be equal and opposite to that of the baseball.

Step 4: Calculate the recoil speed (v) of the pitcher. We know his momentum (p) is -6.0125 kgm/s and his mass (m) is 86.0 kg. So, v = p / m. For the pitcher, v = -6.0125 kgm/s / 86.0 kg = -0.06991627907 m/s.

The negative sign indicates that the direction of the pitcher's motion is opposite to that of the baseball's motion, as expected. So, the pitcher's recoil speed is 0.0699 m/s.