A baseball has a mass of 155 g, and a top major league pitcher can throw it at 41.0 m/s. If an 82.0 kg pitcher was standing on a sheet of ice and then threw the ball, what would his recoil speed be? 21.7 cm/s 12.9 cm/s 77.5 cm/s 7.75 cm/s
Question
A baseball has a mass of 155 g, and a top major league pitcher can throw it at 41.0 m/s. If an 82.0 kg pitcher was standing on a sheet of ice and then threw the ball, what would his recoil speed be? 21.7 cm/s 12.9 cm/s 77.5 cm/s 7.75 cm/s
Solution
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 a momentum of mass_ball * velocity_ball and the pitcher has a momentum of mass_pitcher * velocity_pitcher.
Setting these two equal gives us:
mass_ball * velocity_ball = mass_pitcher * velocity_pitcher
We can solve for the velocity of the pitcher (recoil speed) by rearranging the equation:
velocity_pitcher = (mass_ball * velocity_ball) / mass_pitcher
Substituting the given values:
velocity_pitcher = (0.155 kg * 41.0 m/s) / 82.0 kg = 0.0775 m/s
Converting this to cm/s (since the options are given in cm/s), we get:
0.0775 m/s * 100 = 7.75 cm/s
So, the recoil speed of the pitcher would be 7.75 cm/s.
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